Question

Each of ten large barrels is filled with golf balls that all look alike. The balls in nine of the barrels weigh 1 ounce and the balls in one of the barrels weigh 2 ounces. With only one weighing on a​ scale, how can you determine which barrel contains the heavy golf​ balls?

Choose the correct answer below.

A. Weigh all of the balls from only one barrel to narrow down the selection of barrels that may contain the heavier balls.

B. Select one ball from the first​ barrel, two balls from the second​ barrel, and so​ on, up to ten balls from the tenth barrel to find the weight of a specific number of balls in a specific barrel.

C. Weigh all of the balls from all ten barrels to find the average weight of the balls in all ten barrels.

D. This is not possible. There is no way to determine which barrel contains the heavy golf balls.

Answer 1

B will be the right answer,

There may be more then one solution to this problem, but here is the one that I came up with.

Let us number the barrels 1 through 10, just to be able to tell thdm apart.

Then take one ball from the 1^st barrel, two from the 2^nd barrel, three from the 3^rd barrel, and so on, until the 10^th barrel.

Then weight the balls we removed together.

If the total weight is 46 ounces, then the first barrel held the heavy golf balls,

Here we can show that,

= (1×2)+2+3+4+5+6+7+8+9+10

=46

If the total weight is 57 ounce then, the 2^nd barrel held the heavy golf balls,

Here we can show that,

=1+(2×2)+3+4+5+6+7+8+9+10

=57

If thd total weight is 58 ounce, then the 3^rd barrel held the heavy golf balls,

Here we can show that,

=1+2+(3×2)+4+5+6+7+8+9+10

=58

Hence by the calculating further we can get the weight for othe barrels as well.