1959 AMC 12 Problem 19

Attempt Problem 19 of the 1959 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 1959 AMC 12 solutions, or check the answer key.

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

19.

With the use of three different weights, namely,

1

lb.,

3

lb., and

9

lb., how many objects of different weights can be weighed, if the objects to be weighed and the given weights may be placed in either pan of the scale?

15

13

11

9

7

Answer: B

Concepts:number base systematic listing

Difficulty rating: 1360

Small hint:

Each weight may go with the object, against the object, or remain unused

Big hint:

The weights

1,3,9

can represent every integer from

1

through their sum

Solution:

Using coefficients

-1,0,1

for the weights

1,3,9,

balanced ternary represents every integer weight from

1

through

1+3+9=13.

Thus there are

13

different positive object weights that can be measured.

Therefore, the correct answer is B.