The Mathematics of Game Shows - Patterns in Practice

Bingo

42 60 5 30

o 365

Remember: if you are
one away, STAND
UP.

Is the next ball higher
or lower than 30?

Bingo

42 60 5 30
46

o 365

Is the next ball higher
or lower than 46?

Bingo

42 60 5 30
46 24

o 365

Is the next ball higher
or lower than 24?

Bingo

42 60 5 30
46 24 1

o 365

Is the next ball higher
or lower than 1?
(Don’t think too hard

about this one.)

Bingo

42 60 5 30
46 24 1 47

o 365

Remember: if you are
one away, STAND
UP.

Is the next ball higher
or lower than 47?

Bingo

42 60 5 30
46 24 1 47
64

o 365

Is the next ball higher
or lower than 64?

Bingo

42 60 5 30
46 24 1 47
64 39

o 365

Is the next ball higher
or lower than 39?
(What would you do

here? This one is
kind of in the middle.)

Bingo

42 60 5 30
46 24 1 47
64 39 72

o 365

Is the next ball higher
or lower than 72?

Bingo

42 60 5 30
46 24 1 47
64 39 72 56

o 365

Getting closer…?
Is the next ball higher
or lower than 56?

Bingo

42 60 5 30
46 24 1 47
64 39 72 56
67

o 365

Is the next ball higher
or lower than 67?

Bingo

42 60 5 30
46 24 1 47
64 39 72 56
67 41

o 365

Is the next ball higher
or lower than 41?

Bingo

42 60 5 30
46 24 1 47
64 39 72 56
67 41 18

o 365

Is the next ball higher
or lower than 18?

Bingo

42 60 5 30
46 24 1 47
64 39 72 56
67 41 18 3

o 365

Bad time for such a
low number!

Is the next ball higher
or lower than 3?

Bingo

42 60 5 30
46 24 1 47
64 39 72 56
67 41 18 3
48

o 365

Is the next ball higher
or lower than 48?

Bingo

42 60 5 30
46 24 1 47
64 39 72 56
67 41 18 3
48 71

o 365

Is the next ball higher
or lower than 71?

Bingo

42 60 5 30
46 24 1 47
64 39 72 56
67 41 18 3
48 71 26

o 365

(At NCTM 2011, the
contestant won with
this ball.)

Bingo 365

Did strategy change a
One strategy is to go h
half, otherwise lower.
strategy? Or what?
What’s this got to do w
Balance? Similar trian
Players did not follow
actual show: the first c
365 picked “lower” on

5 Strategy

as the game went on?
higher if in the bottom
Is this the best

with summations?
ngles??
good strategy on the
contestant to play Bingo
a 30. (He lost.)

More to

Many related topics ar
Project Precalculus, an
Math Institute material

www.mathforum.org/pcmi

•  How can spinners or
by polynomials?
•  How would expected
Plinko board were rea
•  Would it be reasonab
to win Any Number by

Explore

re asked about in CME
nd in the Park City
ls at

i/hstp/sum2007/morning

r dice be represented

d value change if the
ally, really tall?
ble for 30 of 100 people
y chance? 35? 40?

Thanks and
Any que

Bowen
Research Sc

(and part-time g

bkerins@
www.edc.o

d good luck!
estions?

n Kerins
cientist, EDC

game consultant)

@edc.org
org/cme/mpi