# Transcript: Finale | Mar 26, 1999

A title reads “TVO’s Virtual Classroom. Get connected.” The “V” in “Virtual” is a tick, the “A” in “classroom” is an “at sign” with an extended loop that turns into a power cord with a plug at the end, and the first “O” in “classroom” is a spinning globe.(Lively music plays)

In front of a world Atlas spread on the wall, Mister C., curly-haired and bearded in his forties, with glasses, wearing a burgundy sweatshirt over a white T-shirt, says

HI AND WELCOME TO THE

LAST CLASS OF THE GRADE 9

MATH MYSTERY SERIES.

THE WEATHER'S GOT TO

BE GETTING ALL OF US.

IT'S REALLY, REALLY A

MESS HERE IN TORONTO

AND I WOULDN'T BE

SURPRISED IF YOU'RE HAVING

THE SAME KIND OF

DIFFICULTIES OUT THERE

IN THE REST

OF ONTARIO.

WHAT I'M GOING

TO DO TODAY IS,

I AM GOING TO GO THROUGH

THE PROBLEMS AND MAKE SURE

THAT YOU HAVE A SENSE

OF THE CORRECT ANSWERS,

AND AT THE END

OF THE PROGRAM,

WE WILL DO A WRAP ON THE

MYSTERY JUST SO YOU KNOW

WHAT SHOULD HAVE

HAPPENED AND DID HAPPEN

WITH THE KIDNAPPING

OF DONNY GROVER.

I'M GOING TO START OFF

RIGHT AWAY WITH A PROBLEM

THAT I INTRODUCED

LAST WEEK CALLED

THE COIN PROBLEM,

AND THIS IS IT.

A sheet of paper appears with two loonies and two nickels on it. It also features an S-shaped, six-square grid with two circled letters “P” and two letters “N” inside the four central squares of the grid. The text reads “The Fewest Moves - Horizontal, Vertical or Diagonal to reverse the positions of the pennies and the nickels.”

Mister C. continues THE FEWEST MOVES, AND THE

IDEA WAS TO MOVE SOME COINS

AND I'M GOING TO USE THESE

TWO LOONIES TO SIMULATE

PENNIES AND THESE TWO

NICKELS TO SIMULATE NICKELS.

He moves the loonies to the top squares and the nickels to the bottom ones.

Mister C. continues AND THE IDEA IS TO

REVERSE THE POSITION

OF THE LOONIES AND THE

NICKELS WITH THE FEWEST

NUMBER OF MOVES.

NOW, YOU'RE ALLOWED

TO MAKE DIAGONAL

MOVES LIKE THIS ONE.

THAT ONLY

COUNTS AS ONE.

AND YOU'RE ALLOWED TO MAKE

VERTICAL MOVES LIKE THAT ONE.

AND A HORIZONTAL

MOVE LIKE THAT ONE.

NOW, SOME STUDENTS THOUGHT

THAT THE BEST SOLUTION

WAS SIX, AND THAT'S

RELATIVELY EASY TO DO.

LET'S SEE IF I CAN DO IT

RIGHT BECAUSE WHEN YOU

DO SIX SOMETIMES I GET

THE BETTER ANSWER

BUT LET'S SEE WHAT

HAPPENS HERE.

THAT'S ONE MOVE.

TWO MOVES.

THREE MOVES.

FOUR MOVES.

FIVE MOVES.

SIX MOVES.

YUP, DEFINITELY

YOU CAN DO SIX.

NOT TOO MUCH

DOUBT ABOUT IT.

HOWEVER, IT ACTUALLY CAN

BE DONE WITH FIVE MOVES

IF YOU PLAN A LITTLE

BIT MORE CAREFULLY.

IT'S NOT TOO MUCH DOUBT

THE DIAGONAL MOVE IS

A VERY EFFECTIVE MOVE, SO IF

YOU PUT THAT ONE THERE,

THAT'S ONE MOVE.

He moves the left loonie diagonally to the bottom left square.

BUT INSTEAD OF DASHING

THIS ONE OUT OF THE WAY,

ONE THING YOU

CAN DO HERE IS,

YOU WANT TO LEAVE THAT

SPACE OPEN EVENTUALLY,

SO I'M GOING TO

MOVE THIS NICKEL

INTO THAT

POSITION THERE.

He moves the right nickel diagonally upward to the vacated space.

Mister C. continues SO THAT'S THE

SECOND MOVE.

THE THIRD MOVE WOULD

PULL THIS LOONIE

DOWN INTO THAT SPOT.

He moves the right loonie down to the spot vacated by the nickel.

Mister C. continues FOURTH MOVE, AH, WE GOT

THE NICKELS IN PLACE AND

LAST, BUT NOT LEAST, THE

FIFTH MOVE AND WE HAVE

THE NICKELS AND THE

LOONIES IN PLACE.

He moves the left nickel up, and the loonie on the left into the vacated space, effectively reversing the initial position of the coins.

Mister C. continues BUT YOU KNOW, I DID GET AN

ANSWER FROM A STUDENT

THAT SENT ME A FAX JUST

A LITTLE WHILE BACK

THAT I THOUGHT WAS

ABSOLUTELY BRILLIANT.

HE SAID YOU CAN DO

THIS IN ONE MOVE.

THINK ABOUT IT FOR

A MOMENT OR TWO.

ONE MOVE.

HOW COULD YOU DO

IT IN ONE MOVE?

HOW ABOUT THIS WAY?

He turns the sheet of paper upside down.

Mister C. continues THERE IT IS,

ONE MOVE.

I HAVE A SECOND

PUZZLE TODAY.

THIS IS THE LAST

ONE OF THE SEASON

IN TERMS OF

LITTLE PUZZLES.

IT'S CALLED EQUAL SHARES

AND HERE'S HOW IT READS.

He reads off the text and says “a farmer and a friend bought an 8-litre container of apple cider. They wanted to share the cider equally. Four litres apiece, obviously, but only had a 3-litre and a 5-litre container. How did they do it?”

A sheet of paper shows three rectangular container shapes of different heights marked 8, 5 and 3 litres, and has some mobile rectangles representing one litre attached to it with a paper clip.

Mister C. continues NOW, YOU GOT TO REMEMBER

THAT IN MY CONTAINERS HERE

THAT THEY HAD NO WAY OF

KNOWING WHAT 2 LITRES WAS

OR ANYTHING LIKE THAT

BECAUSE THERE REALLY

WERE NO MARKS.

BUT TO SIMULATE

THE PROBLEM,

WHAT I'VE DONE IS I'VE CUT

A SERIES OF RECTANGLES

WHICH EACH REPRESENT

A SINGLE LITRE.

THE FARMER AND THE

FRIEND WOULDN'T

HAVE BEEN ABLE TO SEE THIS,

PER SE, BUT THEY HAD

TO COME UP WITH AN

INGENIOUS WAY OF MOVING

THE LIQUID AROUND

USING FULL CONTAINERS,

AND THAT'S THE KEY.

He stacks the mobile litre shapes inside the 8-litre container.

Mister C. continues FIRST MOVE HERE,

I WONDER WHAT

IT MIGHT BE.

YOU ONLY HAVE

TWO OPTIONS.

THAT IS TO MOVE THREE

INTO THE THREE

OR FIVE INTO THE FIVE.

LET'S TRY FIVE

INTO THE FIVE.

He moves the five litre shapes into the next container.

Mister C. continues HELLO, STRATFORD, I HEAR

YOU'RE WITH US TODAY.

AH, THAT'S GREAT.

YOU KNOW, I'D LOVE TO

TAKE A CALL RIGHT NOW.

CAN YOU LET ME KNOW WHAT

THE WEATHER'S LIKE

IN STRATFORD?

GIVE ME A CALL.

I WOULD LOVE

TO KNOW.

AH, WE'VE GOT

SOMEBODY CALLING.

THAT'S GREAT.

NOW, OH, WE'VE GOT A

WHOLE BUNCH OF CALLS.

WELL WE MIGHT AS WELL

HAVE A QUICK CHAT HERE

JUST TO GET THE

WHOLE DAY ROLLING.

A voice says HELLO.

Mister C. continues HELLO, IS IT JORDAN?

Jordan says YEAH.

Mister C. continues OKAY, WHAT'S THE WEATHER

LIKE IN STRATFORD?

Jordan says IT'S LIKE A

BLIZZARD HERE.

IT'S REALLY SNOWY.

IT'S BEEN LIKE SNOWING

FOR THREE DAYS STRAIGHT.

Mister C. continues THREE DAYS STRAIGHT.

Jordan says SNOW BANKS ARE LIKE

UP TO THE TOP OF ME.

THEY'RE TALLER THAN ME.

Mister C. continues WOW.

CAN YOU TELL ME, DO YOU

HAVE TO COME IN BY BUS

OR DO YOU LIVE

RIGHT IN TOWN?

Jordan says I WALK TO SCHOOL.

Mister C. continues IS IT VERY FAR?

Jordan says I DON'T KNOW, LIKE

HALF AN HOUR WALK.

Mister C. continues WAS IT REALLY

COLD THIS MORNING?

Jordan says YEAH, I WAS FREEZING.

Mister C. continues WOW.

IT SOUNDS LIKE

HERE IN TORONTO.

INTERESTINGLY ENOUGH, I

THINK A BIG CITY REALLY

GET HITS HARDER IN THE

SENSE THAT THERE'S SO MANY

PEOPLE TRYING TO MOVE

AROUND THAT THEY JUST

CAN'T DO IT AND IT'S

REALLY AWFUL HERE

IN TORONTO RIGHT NOW.

THANK YOU VERY

MUCH, JORDAN.

MAYBE WE CAN TALK TO

SOMEBODY ELSE THAT'S

PHONED IN AND FIND OUT

WHAT THEIR EXPERIENCE

IS LIKE RIGHT NOW.

A voice says HELLO.

Mister C. continues HI, IS IT JENNIFER?

Jennifer says YUP.

Mister C. continues OKAY, SO WHAT'S

IT LIKE FOR YOU?

Jennifer says IT'S COLD.

Mister C. continues IT'S COLD.

BY ANY CHANCE, ARE YOU

BUSING IN OR WALKING IN?

Jennifer says I WALKED.

Mister C. continues OKAY.

ABOUT HOW MUCH

TIME IN THE SNOW?

Jennifer says IT CAN - IT DOES

NOT TAKE AN HOUR.

[laughing]

Mister C. continues WOW.

Jennifer says IT CAN TAKE ABOUT

HALF AN HOUR.

Mister C. continues HALF AN HOUR STILL ON

TIME OUT IN THIS COLD.

DO YOU LIKE SKIING

BY ANY CHANCE?

Jennifer says NO.

Mister C. continues AH, THAT'S TOO BAD.

I THINK THE SKIERS ARE

JUST LOVING

WHAT THEY'RE SEEING, EH?

She says YEAH.

Mister C. continues OKAY.

I'LL TAKE ONE

MORE CALL ANYWAY.

AND THEN I WANT YOU PEOPLE

TO CALL IN ABOUT

THE MATH

AFTERWARDS, SO.

LET'S SEE, IS

IT JOEL?

Joel says HELLO.

Mister C. continues HI, JOEL.

Joel says YEAH.

Mister C. continues SO WHAT'S YOUR

EXPERIENCE LIKE?

Joel says IT'S COLD.

[laughing]

Mister C. continues NO KIDDING, WALKING

OR BUSING AGAIN?

Joel says I WALKED.

Mister C. continues PRETTY TOUGH DOWN

THERE IN STRATFORD,

ALL YOU GUYS,

I GUESS, EH?

Joel says YEAH.

Mister C. continues WELL, THANK YOU VERY

MUCH FOR CALLING, JOEL.

Joel says OKAY.

Mister C. continues AND I'M GOING TO GO

BACK TO THE PROBLEM NOW.

YOU CAN SEE IT, EH?

I'VE STARTED THE

PROBLEM AND LET'S

SEE IF THE FOUR OF YOU

AND ANYBODY ELSE

THAT'S IN THE CLASSROOM

RIGHT NOW CAN GIVE ME

A HAND WITH THIS.

WHAT I'D LIKE TO DO IS

TALK TO ONE OF YOU

AND YOU SUGGEST TO ME

WHAT I SHOULD DO NEXT.

I'VE GOT 3 LITRES LEFT

OVER IN THIS 8-LITRE

BARREL AND I'VE GOT

5 SITTING THERE.

NOW, I'LL GO BACK TO

SQUARE ONE AND WHAT

I'LL DO IS I'LL

RE-EXPLAIN THE PROBLEM.

HERE IT IS.

He produces the first sheet of paper again and reads off it.

Mister C. continues THE PROBLEM IS

CALLED EQUAL SHARES.

THE FARMER AND HIS FRIEND WANT TO

SHARE THE CIDER EQUALLY, WHICH

OBVIOUSLY MEANS

4 LITRES APIECE.

WITH ONLY A 5-LITRE AND A 3-LITRE

CONTAINER HOW DID THEY DO IT?

AND I STARTED OUT WITH 8

LITRES IN THE BIG BARREL

HERE SO TO SPEAK.

NOW, REMEMBER THAT THE

FARMER AND HIS FRIEND

CAN'T SEE THESE

LITTLE DIVISIONS.

I'M JUST DOING THIS SO

THAT WE CAN ACTUALLY

SEE AND UNDERSTAND THE

SOLUTION TO THE PROBLEM.

OH, GOOD, I THINK JORDAN'S

PHONING IN AND WE'LL

SEE IF WE CAN'T FINISH

THIS PROBLEM OUT.

AND JUST A SECOND OR TWO

WE WILL BE CONNECTED.

I WONDER WHAT WE

SHOULD DO NEXT.

Jordan says HELLO.

Mister C. continues HI, JORDAN.

Jordan says HI.

Mister C. continues WHAT DO YOU THINK WE

SHOULD DO NEXT, JORDAN?

Jordan says WELL, IF THEY WANTED,

THEY COULD PUT 4 LITRES IN

THE 5 LITRES AND 4 LITRES

IN THE 8 LITRES AND ONE

PERSON COULD DRINK FROM

8 LITRES AND FORGET

THE 3 LITRES.

Mister C. continues HANG ON, SLOW

DOWN A BIT, JORDAN.

EXACTLY WHAT DO I DO?

HOW DO I DO THIS?

Jordan says OKAY, PUT ONE OF THE

5 LITRES BACK

IN THE 8 LITRES.

Mister C. continues AH, OKAY, IT SOUNDS GOOD.

THE PROBLEM,

JORDAN, IS THIS.

NOW, STAY WITH ME.

IS THAT THE FARMERS

CAN'T ACTUALLY

SEE THESE DIVISIONS.

I DID IT SO THAT WE COULD

SORT OF SEE HOW THE

PROBLEM LOOKS IF YOU

KNEW BUT THEY WERE -

Jordan says BUT THEY COULD GET

A MEASURING CUP.

Mister C. continues THAT WOULD BE NICE

BUT WE DON'T HAVE ONE.

Jordan says AH, COME ON.

Mister C. continues WE DON'T NEED ONE,

THOUGH, YOU SEE, JORDAN.

THAT'S THE TRICK.

Jordan says ALL RIGHT.

Mister C. continues REMEMBER WHAT WE NEED

ARE FULL CANISTERS.

IF I WAS TO FILL THIS

3-LITRE CANISTER,

WHERE WOULD I STEAL MY

3 FROM, HERE OR HERE?

He points to the large canister with three litres in it and the medium one which is full with 5 litres in it.

Mister C. continues WHAT DO YOU THINK?

Jordan says THE 8 LITRE.

Mister C. continues -NOW, IF I DO THAT, IS

IT GOING TO HELP ME?

Jordan says NO.

Mister C. continues SO LET'S TRY THE

OTHER ONE, EH?

Jordan says THE 5, YEAH.

Mister C. continues OKAY.

NOW IS THERE SOMEBODY

ELSE CALLING IN?

I'LL TELL YOU

WHAT, JORDAN,

I'M GOING TO LET

YOU OFF THE HOOK.

Jordan says YEAH, CALL

SOMEBODY ELSE.

Mister C. continues JUST THIS ONCE AND WE'LL

TALK TO JENNIFER, I THINK.

I ALWAYS HAVE TROUBLE

READING THE SCREEN SOMETIMES.

JENNIFER?

Jennifer says YEAH?

Mister C. continues OKAY.

THIS IS A GOOD SITUATION.

SO FAR WE'RE

PROCEEDING ALONG.

ANY IDEA WHAT YOU

SHOULD DO NEXT?

TRICKY LITTLE

PROBLEM, ISN'T IT?

She says WELL, I HAD IT FIGURED

OUT AND NOW I JUST FORGOT.

OH, OKAY, IF YOU PUT --

OH, WAIT, NEVER MIND.

Mister C. continues I'M GOING TO GIVE

YOU A BIT OF A HINT.

STAY WITH ME, JENNIFER.

She says OKAY.

Mister C. continues SEE THIS 3 LITRES RIGHT

HERE THAT YOU NOW

KNOW IS 3 LITRES

BECAUSE IT'S FULL?

She says MM-HMM.

Mister C. continues I WON'T PUT IT BACK HERE.

OBVIOUSLY WHERE I AM

GOING TO PUT IT BACK.

She says PUT IN THE

8 LITRES.

Mister C. continues OKAY.

NOW, WHAT WE'VE

ACCOMPLISHED DOING HERE IS

WE NOW HAVE A

DIFFERENT SPLIT.

WE ACTUALLY HAVE 6 SITTING

IN HERE IF WE'VE DONE THE

MATH AS WE WENT

ALONG, RIGHT?

AND WE GOT TWO IN HERE.

NOW, CAN YOU SUGGEST WHAT

THE NEXT MOVE MIGHT BE?

She says PUT 2 LITRES

FROM THE 8 LITRE --

Mister C. continues REMEMBER YOU CAN'T SEE

THAT BUT THESE 2 LITRES

DOWN HERE, WHERE

MIGHT I PUT THEM.

She says 2 LITRES FROM THE 5

LITRE INTO THE 3 LITRE.

Mister C. continues BINGO.

NOW, TELL ME MY

NEXT MOVE.

PUT 1 LITRE OR

FILL UP THE 3 LITRE.

Mister C. continues NOT YET.

YOU'RE ONE MOVE

EARLY ON THAT.

She says FILL UP THE 5.

Mister C. continues FILL UP THE 5 AND YOU

SEE WHY THAT WORKS OUT?

TAKE A LOOK AT WHAT I

ENDED UP WITH

HERE AT THE BOTTOM.

He points to one litre in the 8-litre canister.

She says I SEE.

Mister C. continues SO WHAT I DO IS, I FILL

UP THE 5 AND THEN I

POUR OFF FROM HERE.

REMEMBER, I'VE GOT 5 IN

HERE BUT I GOT 1 EXTRA HERE.

She says YEAH, I SEE NOW.

Mister C. continues I POUR OFF 1 IN HERE.

He takes one litre off the top of the 5-litre canister and puts it in the now full 3-litre one, leaving 4 litres in the 5-litre canister.

She says YEAH, AND THEN

PUT THEM IN -

Mister C. continues PUT THE 3 BACK HERE

AND YOU GOT THE

SOLUTION.

YOU SEE THAT?

AND YOU'VE GOT THE SOLUTION.

He adds the contents of the 3-litre canister to the litre remaining in the 8-litre one.

She says YEAH.

Mister C. continues ALL IT TAKES IS A LITTLE

BIT OF TRIAL AND ERROR.

THANK YOU VERY

MUCH, JENNIFER,

YOU WERE A GREAT

HELP ON THAT.

IT'S NOT SIMPLE AND

WHEN I POSE THE PROBLEMS

OBVIOUSLY IN THIS FORMAT

IT'S SOMETHING WHERE

YOU'RE UNDER A LITTLE BIT

OF PRESSURE AND SOMETIMES

IT'S NOT SO EASY TO DO IT

AS QUICKLY AS I WOULD LIKE

YOU TO DO IT ON AIR.

NOW, WHAT I'M GOING TO DO

AND I'M NOT QUITE SURE,

I WOULDN'T MIND YOU

TELLING WHEN YOU FIRST

PHONE IN, I'M TAKING

UP THE PROBLEMS

FROM LESSONS 10 AND 11.

NOW, I WILL ONLY DO A

SELECTED SET OF PROBLEMS.

I'M GOING TO TRY TO PICK

OUT THE ONES THAT

ARE RATHER INTERESTING OR

HAVE SOME IMPORTANT THINGS

TO SAY ABOUT THEM.

IN AS MANY CASES

AS POSSIBLE,

I'M GOING TO INVITE

YOU TO HELP ME OUT.

AND THE MORE YOU

HELP ME, THE MORE

YOU'LL GET OUT OF THIS.

SO I'M GOING TO START

WITH EXERCISE NUMBER 10.

AND THAT PARTICULAR

EXERCISE STARTS

WITH A PROBLEM THAT

SOUNDS LIKE THIS.

A sheet of paper appears and he reads off it and says “How many different outfits can you wear to school if you have - a) 12 tops, b) 4 different pairs of pants and c) 11 different pairs of socks. Explain your reasoning.”

Mister C. continues NOW, FIRST OF ALL,

HAS ANYBODY GOT

THE ANSWER TO

THE PROBLEM?

BUT EVEN IF YOU DON'T,

HAVE YOU GOT SOME SENSE

OF HOW YOU MIGHT FIND THE

ANSWER, EVEN IF YOU DON'T

HAVE AN ACTUAL NUMBER DOWN

ON THE PIECE OF PAPER?

LET'S THINK ABOUT THIS

FOR A MOMENT OR TWO.

ONE OF THE WAYS TO BEGIN

TO UNDERSTAND THE PROBLEM

IS TO TAKE A

SMALLER PROBLEM.

WHAT IF, FOR INSTANCE,

INSTEAD OF 12 TOPS,

I ONLY HAD 2.

INSTEAD OF 4 DISTINCT

PAIRS OF PANTS, I HAD 3.

AND LET'S SAY

WITH THE SOCKS,

I HAVE 2 PAIRS

OF SOCKS.

NOW HOW MANY DIFFERENT

WAYS CAN I CREATE

AN OUTFIT WHICH INCLUDES,

OBVIOUSLY, A TOP,

A PAIR OF PANTS,

AND A PAIR OF SOCKS?

I'M GOING TO GO

THE OTHER WAY.

I DON'T WANT TO

EMBARRASS YOU AT ALL,

BUT I'M GOING TO GET

SOMEBODY TO HELP ME OUT

AND LET'S SEE, I'M

GOING TO TRY TO WORK

WITH JOEL THIS TIME.

SO WE'LL CALL

OUT TO JOEL.

AND JUST WORK

WITH ME.

AS I SAY, WE'RE JUST

WRAPPING THIS UP AND

THE MORE INFORMATION I CAN

GET TO YOU, THE BETTER.

WE'LL BE CONNECTED TO JOEL

IN JUST A MOMENT OR TWO.

THE REST OF YOU, THINK

ABOUT THIS, AS WELL.

I MEAN, YOU CAN

SUPPORT JOEL IF YOU -

A voice says HELLO.

Mister C. continues HI, JOEL.

Joel says HELLO.

Mister C. continues HAVE YOU GOT ANY IDEA

HOW TO SOLVE THE SIMPLE

PROBLEM, WHEN THERE'S 2

TOPS, 3 PAIRS OF PANTS,

AND 2 PAIRS OF SOCKS?

Joel says I'LL MAKE A CHART.

Mister C. continues OKAY, YOU COULD DO THAT.

SO LET'S SAY YOU HAD

A BLUE AND A RED TOP.

YOU HAD, OH, HOW

SHALL WE DO THIS.

BEIGE, WELL, BROWN, WE

COULD PUT B-R AND MAYBE

BLACK, AND THEN WE HAD,

OH, TERRIBLE SELECTION,

WHITE SOCKS OR

YELLOW SOCKS. OKAY?

SO WHAT WOULD YOU

DO TO START IT?

WHAT COMBINATION

WOULD YOU START WITH?

Joel says BLUE TOP.

BLACK PANTS.

Mister C. continues BLACK PANTS, YUP.

Joel says AND WHITE SOCKS.

Mister C. continues AND SO ON.

OKAY, GIVE ME ONE

MORE SELECTION.

Joel says BLACK TOP, BEIGE.

Mister C. continues BEIGE, THAT WAS THE

FIRST ONE I USED, YUP.

Joel says AND YELLOW SOCKS.

Mister C. continues AND SO ON.

AND IF YOU GOT

EVERY ONE OF THOSE,

YOU'D GET THE

ANSWER, WOULD YOU?

Joel says YES.

Mister C. continues OKAY.

CAN YOU TELL ME OR GIVE

ME SOME SENSE OF WHERE

YOU MIGHT

CALCULATE THAT?

HOW MANY WAYS CAN

YOU PICK A TOP?

Joel says FIVE?

Mister C. continues NO, JUST TWO.

Joel says OH, TWO.

OH, OKAY.

Mister C. continues HOW MANY WAYS OF

PICKING THE PANTS?

Joel says THREE.

Mister C. continues OKAY.

HOW MANY COMBINATIONS

WOULD YOU GET WITH

JUST THE TOP

AND THE PANTS?

Joel says I DON'T KNOW.

Mister C. continues WELL, THERE'S ONLY TWO

OPTIONS YOU CAN DO HERE.

Joel says SIX.

Mister C. continues THAT'S RIGHT.

SO YOU MULTIPLIED,

DIDN'T YOU?

Joel says YEAH.

Mister C. continues SO FOR EACH WAY

YOU CAN PICK A TOP,

THERE ARE THREE WAYS

OF PICKING THE PANTS.

NOW WHAT DO YOU DO WITH

THE LAST NUMBER HERE

IF I WANTED A COMBINATION

OF ALL THREE?

THERE'S SIX WAYS

OF DOING THIS.

Joel says YOU TIMES IT BY 2?

Mister C. continues RIGHT.

SO YOU GET A

TOTAL OF 12.

SO 2 TIMES 3

TIMES 2 EQUALS 12.

WELL, WHAT DO YOU THINK

YOU DO WITH THESE NUMBERS?

Joel says TIMES THEM

ALL TOGETHER?

Mister C. continues YOU WANT TO BET.

NOW, THE ONLY TRICK

HERE DOING THAT,

I CAN DO IT WITHOUT

A CALCULATOR.

4 TIMES 12 IS 48

TIMES 11, WELL,

THAT'S 480 PLUS ANOTHER

48, AND THE ANSWER IS 528.

NOW, I GET USED TO DOING

THINGS WITHOUT CALCULATORS

IF I CAN HELP IT.

AND ACTUALLY THAT'S

A GOOD POINT.

THE MORE YOU

CAN DO MENTALLY,

THE BETTER OFF YOU ARE.

OK, WHAT WE'RE GOING TO

DO AT THIS POINT

IS GO TO THE

NEXT QUESTION.

A sheet of paper reads “2. How many ways can you move from point “A” to point “B” on these grids, if you can only travel up or forward?”

The three grids are one, two and three squares, laid out in horizontal lines, with the bottom left corner marked “A” and the top right corner of each grid marked “B.” He appears in a small frame at the bottom right.

Mister C. continues THIS IS A SIMILAR TYPE

OF PROBLEM AND I'VE SORT

OF SET IT UP AS A

SMALL INVESTIGATION.

I'LL INVITE SOMEBODY

TO PHONE IN, IF NOT,

I WILL ASK - I'LL

ACTUALLY CALL OUT

AND I'LL JUST COACH YOU

THROUGH THIS ONE, AS WELL.

IT'S NOT A

TERRIBLY HARD ONE.

OKAY, IT LOOKS LIKE

JORDAN'S CALLING IN.

THAT'S GREAT.

SO THIS IS HOW MANY WAYS

YOU CAN GO FROM A TO B

BUT YOU CANNOT GO BACKWARDS

AND YOU CAN'T GO DOWN.

SO IT'S FAIRLY

STRAIGHTFORWARD AND

WE'LL BE CONNECTED TO

JORDAN IN JUST A SECOND.

THERE YOU ARE.

HI, JORDAN.

Jordan says I'M HERE.

Mister C. continues OKAY.

HOW MANY WAYS OF GOING

FROM A TO B IN THE

VERY FIRST ONE?

Jordan says THREE?

Mister C. continues OKAY, DESCRIBE

THEM FOR ME.

Jordan says OKAY, YOU CAN GO STRAIGHT

UP AND THEN RIGHT.

Mister C. continues YUP, THAT'S ONE.

Jordan says AND THEN YOU CAN

GO LIKE DIAGONALLY.

Mister C. continues OH.

IF THERE'S NO LINE THERE,

WE DON'T COUNT IT.

Jordan says OH, MAN.

Mister C. continues BUT THAT'S COOL.

SO YOU'VE GOT THE

OTHER ONE, AS WELL.

Jordan says YEAH, THAT ONE.

Mister C. continues SO THAT'S TWO.

OKAY, HOW MANY WAYS

OF DOING THIS ONE? (showing the two-box grid)

Jordan says WELL, YOU COULD

DO FOUR?

NO, FIVE?

Mister C. continues LET'S WALK.

YOU TELL ME WHICH

ONES TO SORT OF MARK.

Jordan says STRAIGHT UP.

Mister C. continues STRAIGHT UP?

Jordan says YEAH, AND THEN GO ALL

THE WAY TO THE RIGHT.

Mister C. continues THAT'S ONE.

Jordan says OKAY, AND THEN GO

ALL THE WAY TO RIGHT

ON THE BOTTOM

AND GO UP.

Mister C. continues THAT'S TWO.

Jordan says AND THEN GO

BOTTOM ONE SQUARE,

UP THROUGH THE MIDDLE,

AND THEN OVER TO B.

Mister C. continues HOW MANY IS THAT?

Jordan says THREE.

Mister C. continues NOW, IF YOU WERE TO GUESS

IF I ADD A BOX HERE,

WHAT DO YOU THINK THE

ANSWER TO THIS NEXT ONE

WILL BE? (points to the three-box grid)

Jordan says FOUR.

Mister C. continues AND WE COULD CHECK

THAT OUT REALLY FAST.

UP AND OVER.

UP AND THROUGH THERE.

UP AND THROUGH THERE.

AND OVER THERE.

WELL, WHAT DO YOU KNOW?

SO YOU SEE, IF YOU HAVE

JUST A LONGER AND LONGER BOX,

WE GOT A PATTERN,

DON'T WE?

IS THAT OKAY, JORDAN?

Jordan asks IS THERE ANY OTHER

SCHOOLS INVOLVED TODAY?

Mister C. continues NO, ACTUALLY NOT.

THAT'S WHY I'M TALKING

TO YOU GUYS EXCLUSIVELY.

IS THAT OKAY?

Jordan says OH, OKAY.

Mister C. continues SO YOU GOING TO JUST HAVE

TO GO WITH THE FLOW WITH ME.

NOW, WE'VE GOT TWO MORE.

DO YOU WANT TO HELP ME

ON THIS ONE, JORDAN?

Jordan says YEAH.

Mister C. continues OKAY.

HOW ABOUT THIS ONE?

A new sheet of paper shows two box grids. The top one has four boxes in a square, and the bottom one has six boxes in a horizontal rectangle. As in the previous case the bottom left and top right corners of each grid are marked A and B respectively. Mister C. points to the top one.

Jordan says AH, MAYBE FIVE.

Mister C. continues YOU'RE GOING

TO SAY MAYBE FIVE.

LET'S SEE IF WE

CAN CHECK IT OUT.

WE GOT THE ONE THAT

GOES LIKE THIS, RIGHT?

Jordan says YUP, AND THEN

THE BOTTOM.

Mister C. continues THEN WE CAN DO

THAT ONE, RIGHT?

NOW, TELL ME SOME

OTHER ROUTE I CAN USE.

Jordan says OKAY, GO ONE OVER

ON THE BOTTOM.

Mister C. continues YUP.

Jordan says UP AND THEN TO THE

B, ALL THE WAY UP.

Mister C. continues ALL THE WAY UP,

SO NOW WE'RE AT THREE.

Jordan says YEAH.

Mister C. continues OKAY, SEE IF YOU CAN

GIVE ME ANOTHER ONE.

Jordan says SAME THING BUT GO

RIGHT IN THE MIDDLE.

Mister C. continues THAT'S FOUR.

ANY OTHERS?

Jordan says AND GO UP FROM A AND THEN

GO RIGHT ACROSS ALL THE WAY.

Mister C. continues YUP, SO THAT'S

ANOTHER ONE.

Jordan says AND THEN GO SAME THING,

BUT GO UP IN THE MIDDLE.

Mister C. continues THANK YOU VERY

MUCH, JORDAN,

BUT I THINK OUR

ANSWER IS 6.

THAT'S COOL.

Jordan says YUP, THAT'S COOL.

Mister C. points to the lower grid and continues

WHAT DO YOU THINK THE

ANSWER MIGHT BE HERE.

I HAVEN'T GOT A

PATTERN ESTABLISHED,

BUT IF YOU'RE

WILLING TO GUESS.

Jordan says EIGHT.

Mister C. continues OKAY, SO THAT'S A

GOOD GUESS ACTUALLY.

LET'S REALLY QUICKLY

CHECK IT OUT.

YOUR TECHNIQUE IS TO

DO THE OUTSIDES FIRST.

Jordan says YEAH, I LIKE TO

DO THEM FIRST.

GET THEM OUT

OF THE WAY.

Mister C. continues GET THEM OUT OF THE

WAY, SOUNDS GOOD.

NOW, HOW ABOUT

THIS NEXT?

WE WANT TO GO ACROSS MAYBE

TO HERE AND DO THESE TWO?

Jordan says YUP.

Mister C. continues SO IF YOU DO THAT,

YOU GET TWO MORE.

Jordan says OH, YEAH, DOUBLE.

Mister C. continues OKAY.

THEN WE GO UP -

Jordan says SAME THING - ONE.

Mister C. continues THIS IS GETTING MORE AN

MORE MESSY, ISN'T IT,

BECAUSE THERE'S ONE.

THERE'S TWO, AND

THERE'S THREE MORE.

SO ONE, TWO, THREE.

LET'S SEE WHAT

I HAVEN'T DONE.

I GUESS I HAVEN'T

DONE THIS.

THERE'S ONE, TWO,

THREE MORE THERE.

Jordan says YUP.

Mister C. continues SO I GET A

TOTAL OF TEN.

Jordan says YEAH, I WAS WRONG,

BUT THAT'S COOL.

Mister C. continues BUT YOU KNOW SOMETHING,

YOUR FIRST GUESS THERE,

YOUR FIRST EIGHT IS

NOT A BAD GUESS.

IT'S A REALLY GOOD

GUESS, ACTUALLY.

THANK YOU VERY

MUCH, JORDAN,

AND I'LL GO ONTO SOME

NEW PROBLEMS AND SEE

WHAT WE CAN DO

WITH THESE.

A new sheet reads “1. the following product is missing two digits A. and B. Find A. - B. A multiplication appears. 2. The average of five numbers is 17. if one number is removed, the new average is 14. What number was removed?”

Mister C. continues I CAN SEE THAT I MADE THE

FONT A LITTLE BIT SMALL

BUT WE'LL HAVE TO SORT

OF LIVE WITH THAT

A LITTLE BIT, I GUESS.

THESE PROBLEMS COME

FROM EXERCISE NUMBER 11.

AND WHAT I'LL DO IS,

I'M GOING TO DO A NUMBER

OF THEM WITH YOU AND

ACTUALLY I'LL DO A COUPLE

OF ORAL QUESTIONS IN

A FEW MOMENTS OR TWO

AND JUST SEE WHAT YOU

CAN DO WITH THEM.

NOW, AND IT SAYS WHAT

WE'RE MISSING IS THE a.

HERE, WHICH IS ALSO

THERE, AND THIS b. HERE. OKAY?

SO THEY'RE THE ONES

THAT ARE MISSING.

THAT'S GOOD.

COME IN A LITTLE BIT,

IT'S EASIER TO SEE.

NOW, WHAT NUMBER WOULD

WORK IN BOTH OF THESE

SPOTS HERE? (points to the calculation)

WHAT DIGIT? LET'S SEE.

PHONE IN ANYBODY.

I PREFER NOT TO BE

ARBITRARY AND PICK

ANYBODY AT RANDOM.

HOW ABOUT JENNIFER

GRISWOOD, PHONE IN.

I'LL TELL YOU, THERE

YOU GO, THANKS A LOT.

THIS IS A NICE

LITTLE PROBLEM.

IT'S NOT TERRIBLY

DIFFICULT AGAIN AND

THERE AREN'T A

LOT OF OPTIONS.

SO WHAT WE'RE TRYING TO

DO IS GET A NUMBER

THAT'LL FIT IN BOTH

OF THOSE SPOTS.

Jennifer says HELLO.

Mister C. continues HI, JENNIFER,

THANKS FOR CALLING.

Jennifer says YOU'RE WELCOME.

Mister C. continues OKAY.

WHAT DO YOU THINK MIGHT GO

IN THAT a SLOT RIGHT

THERE SO THAT THE

MULTIPLICATION WOULD WORK?

Jennifer says UMM, 5.

Mister C. continues 5 MIGHT WORK, SO LET'S

JUST TAKE A LOOK AT

WHAT HAPPENS THERE

IF IT'S A 5.

SO THAT'S A

15, RIGHT?

Jennifer says MM-HMM.

Mister C. continues FIVE 5s IS 25, SO

THAT FITS.

10 PLUS 2 AND YOU

GOT A 2 THERE.

THESE ARE NOT

THE SAME, RIGHT?

Jennifer says RIGHT.

Mister C. continues OKAY, SO MAYBE 5

ISN'T THE ANSWER.

CAN YOU SUGGEST ONE

MORE ALTERNATIVE?

Jennifer says JUST A SECOND. 7.

Mister C. continues 7, OKAY, LET'S

CHECK IT OUT.

SO WE ADD 25 ON THE TOP

AND WE HAVE 17 HERE.

WE GOT THE 5 THERE.

AH, 175, RIGHT

ON THE BUZZER.

SO YOU HAVE

OBVIOUSLY 25.

WHAT'S THE b GOING

TO END UP BEING?

Jennifer says 4.

Mister C. continues IT'S A 4.

NOW, THE TRICK WITH THE

QUESTION PARTLY WAS

IN THE QUESTION ITSELF.

MANY STUDENTS THAT HAVE

A QUESTION LIKE THIS

ACTUALLY FIGURE OUT THAT a.

EQUALS 7 AND b. EQUALS 4,

BUT THEY DON'T

ANSWER THE QUESTION.

IT SAYS FIND

a. MINUS b.

SO THE REASON THAT I

INCLUDED THIS QUESTION

WAS JUST TO REINFORCE THE

FACT THAT YOU READ

THE QUESTION

REALLY CLOSELY.

Jennifer says UH-HUH.

Mister C. continues SO THE ANSWER

WOULD HAVE BEEN 3.

OKAY?

Jennifer says YUP.

Mister C. continues THANK YOU VERY MUCH.

NOW LET'S GO ONTO THIS

NEXT QUESTION BELOW IT.

He reads the text of Question 2.

He says “The average of five numbers is 17. if one number is removed, the new average is 14. What number was removed?”

Mister C. continues WHAT IS THE NUMBER

THAT WAS REMOVED?

WE JUST GRAP A PIECE OF PAPER HERE.

OKAY, SO WE RID OF

MOST OF THAT GARBAGE.

SO, JENNIFER, YOU

STILL WITH ME?

Jennifer says YUP.

Mister C. continues OKAY.

HOW DO YOU GO ABOUT

SOLVING THIS ONE?

Jennifer says I DON'T KNOW.

Mister C. continues OKAY.

WHAT'S THE DEFINITION

OF AN AVERAGE?

JUST SO I KNOW.

WHEN YOU AVERAGE YOUR

MARKS, WHAT DO YOU DO?

Jennifer says ADD THEM TOGETHER AND

THEN DIVIDE THEM BY

HOWEVER MANY THERE WAS.

Mister C. continues OKAY.

IF YOU KNOW THAT THERE

WERE FIVE NUMBERS

AND THAT THE AVERAGE IS

17, CAN YOU FIGURE OUT

WHAT THE TOTAL

NUMBER IS?

Jennifer says THE TOTAL NUMBER?

Mister C. continues YEAH.

LIKE IN OTHER WORDS,

WHENEVER YOU HAVE A PROBLEM

AND THERE ARE THREE

FACTS INVOLVED IN IT,

IF YOU KNOW TWO OF THEM, CAN

YOU FIND OUT THE THIRD ONE?

Jennifer says YEAH?

Mister C. continues THAT'S RIGHT.

NOW, WHAT YOU NORMALLY

GET WHEN YOU'RE ASKED

AN AVERAGE QUESTION IS,

YOU'RE GIVEN THE NUMBERS

AND OF COURSE YOU KNOW

THE NUMBER OF NUMBERS,

SO WHAT YOU DO IS,

YOU JUST NATURALLY ADD

THEM UP AND DIVIDE

BY THAT NUMBER

AND YOU GET IT.

WHAT YOU HAVE THIS

TIME IS THE ANSWER AND

THE NUMBER OF NUMBERS.

IS THERE ANY WAY TO GO BACK

TO WHAT THE TOTAL IS?

THE AVERAGE IS 17 AND

THERE ARE 5 NUMBERS.

WHAT DO YOU THINK

THE TOTAL MIGHT BE?

DO YOU WANT TO CONFER WITH

ONE OF YOUR COLLEAGUES?

She says THAT'S WHAT

I'M DOING.

Mister C. continues GOOD. GOOD.

She says FIVE 17s.

Mister C. continues FIVE 17s, I THINK

THAT'S WHAT YOU SAID.

YOU'RE ABSOLUTELY RIGHT.

SO THE GRAND

TOTAL IS 85.

NOW, I'M GOING TO SHOW

YOU WHAT YOU'RE TRYING

TO SET UP HERE.

YOU TAKE ONE OF

THE NUMBERS AWAY,

HOW MANY NUMBERS

HAVE YOU GOT LEFT?

She says FOUR.

Mister C. continues OKAY, SO YOU HAVE A NEW

AVERAGE, WHICH IS 14.

WHAT'S THE TOTAL OF

NUMBERS WHEN YOU HAVE

FOUR OF THEM AND THE

AVERAGE IS 14?

SAME IDEA AS THIS ONE.

She says FOUR 14s.

Mister C. continues RIGHT.

SO THAT'S 4

TIMES 14 IS 56.

SO WHAT NUMBER

WAS TAKEN AWAY?

She says WHAT WAS IT?

Mister C. continues THE DIFFERENCE BETWEEN -

She says 29.

Mister C. continues RIGHT ON.

IT'S AN INTERESTING

QUESTION AND IT'S A VERY

IMPORTANT ONE IN TERMS OF

AVERAGE AND I'M GLAD

THAT I WORKED THAT WITH

YOU ALL THE WAY THROUGH.

THANK YOU VERY MUCH.

THIS ONE IS A

NASTY QUESTION.

The new question reads “The symbol (rectangle) represents one or more arithmetic operations. If 5 rectangle 3 equals 6, and 7 rectangle 4 equals 12, and 8 rectangle 7 equals 7, find 6 rectangle 2.”

Mister C. continues DID ANYBODY EVER GET A

CHANCE TO WORK ON THIS ONE?

IT'S ABOUT PATTERNING.

ANYBODY WANT TO HELP

ME WITH THIS ONE?

I'LL TELL YOU WHAT.

I'M GOING TO LET YOU OFF

THE HOOK A LITTLE BIT

BECAUSE YOU GUYS HAVE

BEEN WORKING REALLY HARD.

I KNOW THAT IT'S ONLY

A SMALL GROUP OF YOU.

WHENEVER YOU GET A

QUESTION LIKE THIS,

IT SAYS, WHAT'S GOING ON

WITH THESE TWO NUMBERS

THAT GENERATE A 6 AND

WHATEVER THAT RULE

IS THERE HAS TO BE THE

SAME AS THIS RULE HERE,

HAS TO BE THE SAME AS THIS

RULE HERE, AND SO ON.

NOW, IT'S NOT AN EASY

QUESTION BECAUSE I THINK

WHEN I SAW THIS QUESTION

THE FIRST TIME I HAD

A PRETTY GOOD ANSWER

REALLY QUICKLY,

BUT BELIEVE IT OR NOT,

THE SECOND TIME I SAW

THE QUESTION, I DIDN'T

SEE THE ANSWER.

I COULDN'T REMEMBER

WHAT THE TRICK WAS,

SO TO SPEAK.

IT'S NOT REALLY

EVEN A TRICK.

ONE OF THE THINGS THAT

YOU CAN DO THOUGH IS,

YOU CAN TAKE A LOOK

AT THE RELATIONSHIP

OF CERTAIN NUMBERS,

LIKE THE 3 AND THE 6 (he circles them).

THE INTERESTING SIDE ABOUT

THAT IS THAT 3 DIVIDES

EVENLY INTO 6.

I ALSO NOTE THAT 4

DIVIDES EVENLY INTO 12,

AND 7 DIVIDES

EVENLY INTO 7 (he circles the other numbers).

AND THAT WAS THE

CLUE, ACTUALLY.

WELL, 3 GOES INTO

6 HOW MANY TIMES?

IT GOES IN 2 TIMES.

4 GOES INTO 12

3 TIMES.

7 GOES INTO 7

1 TIME.

He writes the figures 2,3 and 1 on the margin of the calculation linking them to it with little arrows.

Mister C. continues YOU COULD SAY,

SO WHAT?

BUT TAKE A LOOK AT

THE DIFFERENCE

BETWEEN THE 5

AND THE 3.

WELL, IT HAPPENS

TO BE 2.

THE DIFFERENCE BETWEEN THE

7 AND 4 HAPPENS TO BE 3.

THE DIFFERENCE BETWEEN THE

8 AND THE 7 HAPPENS TO BE 1.

IS THIS COINCIDENCE?

AND THE ANSWER IS NO.

SO, IF YOU KNOW THAT

BASICALLY THIS BOX MEANS

SUBTRACT THESE 2 NUMBERS

AND MULTIPLY BY THE LAST ONE,

THEN THE ANSWER WILL

BE 6 MINUS 2 IS 4

TIMES 2 IS 8.

IT'S A NEAT

LITTLE QUESTION.

NOW THIS IS ONE YOU CAN

HELP ME ON BECAUSE

IT'S BASED ON A

DEFINITION.

THERE'S AN AWFUL LOT OF

WORDS UP THERE BUT

I'LL READ IT QUITE

QUICKLY TO YOU.

I THINK YOU MIGHT BE ABLE

TO HELP ME OUT ON THIS ONE.

He reads the text of the question on the new sheet of paper.

He says “5. The number 6 has a very special property. If you list all the factors of 6 except the number 6 itself, you will find that the sum of the factors is 6., i.e., 1,2 and 3 divide 6 evenly, and 1 + 2 + 3 equals 6. and is called a “perfect number.” Which one of the following numbers is also “perfect”? 4, 12, 23, 28, 36.”

Mister C. continues NOW FACTORS ARE NUMBERS

WHICH DIVIDE EVENLY INTO 6.

SO THAT'S CALLED

A PERFECT NUMBER.

YOU'RE LOOKING FOR A

NUMBER WHERE IF YOU ADD

THE FACTORS UP, IT WILL BE

EXACTLY THE NUMBER ITSELF.

LET'S SEE I TALKED TO

JENNIFER THE LAST TIME.

THAT WAS GREAT.

HOW ABOUT THE

OTHER JENNIFER.

JENNIFER GRIFFIN.

OH, WE'VE GOT A

SELECTION OF FIVE HERE,

SO IT'S NOT AN

IMPOSSIBLE TASK.

SO WE'RE LOOKING

FOR ANOTHER NUMBER

WHICH IS CALLED A

PERFECT NUMBER.

WE COULD DO IT BY

TRIAL AND ERROR.

Jennifer says HELLO.

Mister C. continues -HI, JENNIFER.

Jennifer says HI.

Mister C. continues THINK YOU CAN HELP

ME ON THIS ONE?

Jennifer says I CAN TRY.

Mister C. continues THAT'S ALL I WANT.

OKAY, SO DO YOU UNDERSTAND

WHAT A PERFECT NUMBER IS?

Jennifer says YEAH.

Mister C. continues OKAY.

DO YOU KNOW WHICH ONE

IT IS WITHOUT ME EVEN

STARTING TO COACH YOU.

WHAT DO YOU THINK?

Jennifer says 36?

Mister C. continues OKAY, YOU

THINK IT'S 36.

Jennifer says I DON'T KNOW.

Mister C. continues THAT'S NOT

A BAD GUESS.

I HAVE A SUSPICION WHY YOU

MIGHT HAVE GUESSED IT.

TELL ME WHY YOU

THINK IT MIGHT BE 36.

Jennifer says I JUST GUESSED.

Mister C. continues IT MIGHT HAVE HAD

SOMETHING TO DO WITH

THE NUMBER 6,

I THOUGHT.

Jennifer says I DON'T KNOW,

I JUST GUESSED.

Mister C. continues OKAY, FAIR ENOUGH.

WELL, LET'S

CHECK IT OUT.

YOU HELP ME BY TELLING ME

WHAT DIVIDES EVENLY INTO 36.

Jennifer says 1 AND 2 AND 3

AND 4 AND 6 AND 9.

Mister C. continues YEAH.

Jennifer says AND 13.

Mister C. continues NO - THE ONE BEFORE.

NO, 12.

Jennifer says 12.

Mister C. continues THERE'S ONE

MORE ANYWAY.

Jennifer says 18.

Mister C. continues YEAH.

NOW, TAKE A LOOK

AT THAT TOTAL.

YOU GOT 39

THERE ALREADY.

IT'S MUCH BIGGER

THAN 36.

SO IT'S NOT THE

PERFECT NUMBER.

SECOND GUESS.

GO FOR A

SECOND GUESS.

LOOK AT THOSE

NUMBERS.

Jennifer says UMM, 4.

Mister C. continues OKAY, LET'S

CHECK OUT 4.

WHAT DIVIDES

EVENLY INTO 4?

Jennifer says 1 AND 2.

Mister C. continues THAT'S IT,

ISN'T IT?

Jennifer says MM-HMM.

Mister C. continues THAT'S 3.

IT'S NOT THE

SAME AS THAT.

OKAY, WE'RE

NARROWING IT DOWN.

IT'S LIKE DOOR NUMBER

1, 2, OR 3

IN LET'S MAKE A DEAL.

Jennifer says 23.

Mister C. continues WELL, WE'VE GOT

THREE MORE.

WHAT DO YOU THINK?

Jennifer says 12.

Mister C. continues OKAY, 12.

WRONG.

[laughing]

DO YOU WANT TO TRY

A DIFFERENT ONE?

IT'S NOT THIS ONE, I'M

GOING TO GET RID OF THAT

ONE BECAUSE THAT'S

A PRIME NUMBER. (He crosses out 23)

LET'S TRY THIS ONE.

Jennifer says UMM, 28.

Mister C. continues OKAY, LET'S SEE, WHAT

DIVIDES EVENLY INTO 28?

Jennifer says 1, 2, 4, 7,

Mister C. continues YEAH, ONE MORE.

Jennifer says 14.

Mister C. continues RIGHT.

LET'S ADD THEM UP.

Jennifer says 28.

Mister C. continues BINGO.

THANKS A LOT, JENNIFER,

YOU'RE A REAL GOOD SPORT.

Jennifer says I TAKE A BUS.

Mister C. continues OH, HEY, I TALKED

TO EVERYBODY AND

I DIDN'T TALK TO YOU.

WHAT WAS THE BUS RIDE

LIKE THIS MORNING?

Jennifer says PARDON?

Mister C. continues WHAT WAS THE BUS

RIDE LIKE TODAY?

Jennifer says THE BUS WAS

REALLY COLD.

OUR BUS DRIVER DOESN'T

KNOW WHAT THE

WORD HEAT MEANS.

[laughing]

Mister C. continues OH, THAT'S A BIT OF

A PROBLEM, ISN'T IT?

Jennifer says YEAH.

Mister C. continues OKAY.

I'M GOING TO DO ONE

PROBLEM ON THE ORAL.

NOW, I KNOW THERE

ARE FOUR OF YOU.

ACTUALLY, I'M GOING

TO DO PROBLEM NUMBER 2.

I WANT YOU TO READ THE

PROBLEM CAREFULLY.

THINK ABOUT THE ANSWER.

IT'S NOT ONE THAT YOU HAVE

TO DO ANY REAL CALCULATION ON.

IT'S ONE THAT YOU SORT OF

EITHER HAVE A SENSE OF IT

OR NOT, SO WE'RE GOING TO

TRY THIS QUESTION HERE.

THERE IT IS.

A sheet of paper reads “Question number 2 - If a baseball's diameter is exactly double the diameter of a golf ball, how much greater is the volume of the baseball that the volume of the golf ball? 1. 2 times - 2. 4 times.”

Mister C. continues OH, MY GOODNESS, I'VE

TYPED SUCH A LONG

QUESTION, I'VE LOST

SOME OF THE SELECTIONS - ANYWAY.

He reads the text.

Mister C. continues NOW, REMEMBER, THIS SAYS

THAT YOU HAVE TWO SPHERES,

ONE'S DOUBLE THE

DIAMETER OF THE OTHER.

NOW, YOU'RE MISSING

SOME ANSWERS THERE

AND I'M GOING TO GO TO

THE GRAPHICS CAMERA

TO SHOW YOU YOUR

SELECTIONS.

OKAY, SO THERE, I'LL GET

THAT STRAIGHTENED OUT.

On a sheet of paper he writes “1. 2 - 2. 4 - 3. 8 - 4. None of above.”

Mister C. continues SO THERE ARE

THE SELECTIONS.

SO DO YOU THINK THAT THE

VOLUME OF THE BALL

IS TWICE AS BIG,

PRESS 1.

FOUR TIMES AS

BIG, PRESS 2.

EIGHT TIMES AS

BIG, PRESS 3,

AND IF YOU DON'T THINK

ANY OF THOSE ANSWERS

IS CORRECT, PRESS - WELL,

YOU'VE ALL ANSWERED NOW,

SO LET'S TAKE A

LOOK AT YOUR GRAPH. INTERESTING.

The bar graph shows one answer in position 1, two in position 2 and one in position 4.

Mister C. continues ONE PERSON THINKS THAT

THE VOLUME WILL DOUBLE

IF YOU DOUBLE THE DIAMETER.

I'M GOING TO DEMONSTRATE

BACK AGAIN HERE.

THE VOLUME OF THE SPHERE

IS GIVEN BY THE FORMULA - “VOLUME EQUALS FOUR-THIRDS PI R. CUBED,”

NOW LET'S SAY THAT

THIS IS THE VOLUME

OF THE GOLF BALL.

IF THE DIAMETER

IS DOUBLED,

WHAT HAPPENS

TO THE RADIUS?

I'M GOING TO MAKE THAT

A BIT OF A RHETORICAL QUESTION.

IT'S DOUBLED.

SO THIS NEW RADIUS IS

GOING TO BE PLACED THIS WAY.

THE VOLUME OF THE

BASEBALL, STILL 4/3 PI,

THAT DOES NOT CHANGE.

INSTEAD OF 1 RADIUS, YOU

HAVE TWO RADIUSES CUBED.

IF WE DO THE CUBING, YOU

HAVE TO CUBE THE 2 AS WELL,

AND THAT HAPPENS TO

BE THE NUMBER 8, (r CUBED).

NOW, TAKE A LOOK AT THIS

FORMULA AND THIS FORMULA.

THIS IS THE SAME AS THAT.

THAT'S THE SAME AS THAT

AND THAT'S THE SAME AS THAT.

WHAT THIS SAYS IS THAT THE

VOLUME OF THE BASEBALL

IS 8 TIMES BIGGER THAN THE

VOLUME OF A GOLF BALL.

REMEMBER THAT WHEN YOU'RE

COMPARING VOLUMES,

THAT WHAT YOU'RE DOING IS

CUBING THE DIFFERENCE.

NOW, YOU GUYS HAVE BEEN

TREMENDOUS SPORTS.

I'VE GOT TONS MORE

QUESTIONS HERE

THAT I COULD TAKE YOU RIGHT

TO THE END, BUT I DON'T

REALLY WANT TO DO THAT.

I DO WANT TO WRAP UP

THE MYSTERY WITH YOU

JUST SO THAT IF YOU'VE

READ THE ENTIRE STORY,

YOU'LL KNOW THAT THERE'S A

LITTLE BIT OF AN ANSWER.

I WON'T GIVE YOU THE

COMPLETE DETAILED ANSWER,

BUT AT LEAST GIVE YOU A

SENSE OF WHAT'S GOING ON,

AND TO TAKE CARE OF THAT

PROBLEM I'VE INVITED

MY INTREPID PAL BACK

INTO THE STUDIO,

GOOD OLD MARC HERE,

AND THERE HE IS.

A life-sized red-haired and moustachioed rag doll wearing a gray pinstriped coat and a white cap appears beside him, looking at some papers on the desk.

Mister C. continues HI, MARC.

GEE, OUR LITTLE CHAT LAST

WEEK WAS A LITTLE BIT PREMATURE.

I MEAN, WE WERE TALKING

ABOUT IT BEING COLD.

IT'S AWFULLY

COLD OUT THERE.

Inside a white outlined frame on a blackboard, a caption reads “Marc Replies - There is no doubt that it is global “colding”! At least in Toronto.”

Mister C. continues HAVE YOU AND YOUR

PROFESSOR FRIEND FIGURED

OUT THE SOLUTION TO THE

DONNY GROVER KIDNAPPING CASE?

Inside a white outlined frame on a blackboard, a caption reads “Marc Replies - Pretty much.”

Mister C. continues WELL, TELL ME

WHAT THEY FOUND.

Inside a white outlined frame on a blackboard, a caption reads “Marc Replies - As you can see on the map, the kidnappers have been travelling around the world. Some of the places they have visited were intended to throw the authorities off the trail.”

Mister C. turns his chair toward the atlas, pointing to a list of cities.

Mister C. continues OH, I SEE.

THEY'VE BEEN ALL AROUND

THE WORLD, TO TOKYO, MELBOURNE, SHANGHAI SHI, AGRA,

NAIROBI, CANNES, RIO DE JANEIRO, MEXICO CITY.

NEW YORK AND MONTREAL.

BOY WHAT A

TRIP THIS IS. GEE.

I'M BEGINNING TO SEE

WHAT YOU MEAN HERE.

THEY STARTED UP HERE

IN TOKYO AND THEN

DOWN TO MELBOURNE AND

SO ON AND SO FORTH.

I WONDER WHAT

THESE STARS MEAN?

Inside a white outlined frame on a blackboard, a caption reads “Marc Replies - The places with the stars beside them are the ones to note, because they are the locations of the world's major film festivals.”

Mister C. continues EXPLAIN FURTHER, PLEASE.

Inside a white outlined frame on a blackboard, a caption reads “Marc Replies - You see, the motive for the kidnapping was to ensure that Donny Grover's epic edu-documentary would never appear!”

Mister C. continues WHY?

Inside a white outlined frame on a blackboard, a caption reads “Marc Replies - the producers knew that it would be so much better than their films that they had to cheat to win.”

Mister C. continues I SEE.

NO DONNY, NO FILM,

THEY WIN THE PRIZES.

THEY GET THE

CONTRACTS.

HMM, AND THEY MAKE

THE BIG BUCKS.

IS THERE ANY CHANCE OF

CATCHING THESE GUYS?

Inside a white outlined frame on a blackboard, a caption reads “Marc Replies - According to our calculations, the “bad guys” are headed towards Montreal - the site of the last major film festival of the year!!”

Mister C. continues I WONDER IF WE GOT

A SHOT OF MONTREAL.

A clip shows the downtown area, full of skyscrapers.

Mister C. continues AH, THERE IT IS.

WHAT A BEAUTIFUL

TOWN THAT IS.

SO THAT'S HOW IT'S

GOING TO END UP.

THE CULPRITS ARE

HEADING TO MONTREAL

RIGHT AS WE SPEAK.

I'LL TELL YOU WHAT, MARC,

I'M GOING TO INFORM THE RCMP

AND LET THEM KNOW

AND MAYBE

THEY CAN NAB THEM

RIGHT IN MONTREAL.

THANKS FOR

EVERYTHING, MARC.

IT'S BEEN GREAT

TALKING TO YOU.

NOW, BACK TO THE

FOLKS IN STRATFORD.

I CERTAINLY APPRECIATE

YOU'RE WORKING WITH ME TODAY.

HAVE YOU GOT A QUESTION

JUST BEFORE I LEAVE

AND SIGN OFF FOR

THE LAST TIME?

I'LL GIVE YOU ONE MORE

CHANCE TO CALL ME.

IF NOT, I AM CERTAINLY

GOING TO THANK YOU.

HEY, YOU'VE DONE A LOT

OF TALKING TODAY SO

WE'LL JUST TAKE

IT AS SO.

YOU GUYS HAVE

BEEN FABULOUS.

THANK YOU FOR STICKING

WITH ME THROUGHOUT

THE PROGRAM AND I HOPE YOU'VE

LEARNED SOME MATHEMATICS.

THANKS TO YOUR TEACHERS FOR

LETTING YOU PARTICIPATE

AND HELPING YOU IN WHATEVER

WAYS THAT THEY HAVE.

THANK YOU TO THE

FACILITATORS AS WELL.

I KNOW THAT WITHOUT

FACILITATORS THAT WE DON'T

PULL THESE THINGS OFF, AND

ALL THE GUYS THAT WORK

BEHIND THE SCENES HERE,

YOU'D BE AMAZED AT HOW

MANY PEOPLE ACTUALLY PULL

TOGETHER TO PUT THESE

SHOWS ON THE AIR.

I HOPE THAT SOME DAY WE

CROSS PATHS AGAIN AND

WE'LL SEE YOU - OH,

WE'VE GOT A CALL.

I'LL TAKE A CALL.

AND I THINK JENNIFER IS

WHO WE'RE CONNECTING

TO RIGHT NOW.

HI, JENNIFER.

Jennifer says HI.

WE JUST WANT TO SAY THANK

YOU BECAUSE IT WAS LOTS OF FUN.

Mister C. continues I APPRECIATE THAT.

THESE SHOWS ARE

REALLY TRICKY TO DO.

I GUESS AS A TEACHER, THE

TOUGHEST THING FOR ME

IS NOT ACTUALLY

SEEING YOU GUYS.

Jennifer says MM-HMM.

Mister C. continues SO, THANK YOU VERY MUCH

FOR LETTING ME KNOW THAT.

I APPRECIATE

THAT SO MUCH.

Jennifer says YOU'RE WELCOME.

Mister C. continues AND WE'LL TAKE

ANOTHER CALL AS WELL.

JENNIFER, THE OTHER,

JENNIFER GRIFFIN, THAT IS.

Jennifer says HELLO.

I JUST WANTED TO

SAY THANK YOU AGAIN.

Mister C. continues AH, THANK YOU,

ONCE AGAIN,

I REALLY DO

APPRECIATE IT.

I HOPE YOU GET A CHANCE TO

DO SOME MORE THIS WAY

AND MAYBE THE PROGRAM

WILL EXPAND HERE AT TVO.

Jennifer says YEAH, THAT WAS

FUN AND MY BUS,

I HAD TO WAIT OUTSIDE

BECAUSE IT WAS LATE TODAY.

[laughing]

AND THEN I WAS

LATE FOR SCHOOL.

Mister C. continues SO IT'S BEEN A

LONG DAY, HASN'T IT?

Jennifer says YEAH.

Mister C. continues WELL, THANK

YOU, EVERYBODY.

HAVE A SAFE TRIP

HOME TONIGHT.

Jennifer says ALL RIGHT, BYE.

Mister C. continues BYE BYE.

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