1963 AMC 12 Problem 23

Attempt Problem 23 of the 1963 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1963 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

23.

A

gives

B

as many cents as

B

has and

C

as many cents as

C

has. Similarly,

B

then gives

A

and

C

as many cents as each then has.

C

, similarly, then gives

A

and

B

as many cents as each then has. If each finally has

16

cents, with how many cents does

A

start?

24

26

28

30

32

Work backward from the final holdings

Immediately before someone gives, each recipient must have half of the amount held just after that gift

Reverse the transactions. Before

C

gives, the holdings are

(8,8,32).

Before

B

gives, they are

(4,28,16).

Before

A

gives,

B

and

C

must have had

14

and

8,

while

A

had

4+14+8=26.

Therefore, the correct answer is B.

Problem 23 in other years