MathDB

Set 3
3.1 Annie has

24

letter tiles in a bag;

8

C’s,

8

M’s, and

8

W’s. She blindly draws tiles from the bag until she has enough to spell “CMWMC.” What is the maximum number of tiles she may have to draw?
3.2 Let

T

be the answer from the previous problem. Charlotte is initially standing at

(0, 0)

in the coordinate plane. She takes

T

steps, each of which moves her by

1

unit in either the

+x

-x

+y

, or

-y

direction (e.g. her first step takes her to

(1, 0)

(1, 0)

(0, 1)

(0, -1)

). After the T steps, how many possibilities are there for Charlotte’s location?
3.3 Let

T

be the answer from the previous problem, and let

S

be the sum of the digits of

T

. Francesca has an unfair coin with an unknown probability

p

of landing heads on a given flip. If she flips the coin

S

times, the probability she gets exactly one head is equal to the probability she gets exactly two heads. Compute the probability

p

.
PS. You should use hide for answers.

Problem Statement