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Logic Level 2

You have 5 boxes. Each box has 2 balls. One of the boxes have the balls weighing 9 g each. All other balls weigh 8 g each. You have a weighing machine which displays ( the weight on the left pan - the weight on the right pan). What is the minimum number of moves by which you can determine the heavier balls?

1 4 2 3

2 solutions

Marta Reece
Jan 21, 2018

One side: 2 from one box, 1 from another.

Other side: 2 from one box, 1 from another, all boxes different from those above.

If both sides are equal, remaining box has heavy balls.

If difference is 1 g, the box which contributed 1 to the heavier side is it.

If difference is 2 g, it's the box which contributed 2 to the heavier side.

Rajdeep Ghosh
Jan 21, 2018

The question is a variation from the original classical riddle.

Let the boxes be A, B, C, D and E.

We take 0 balls from A.

We take 1 ball from B.

We take 2 balls from C.

We take 1 ball from D.

We take 2 balls from E.

We put the weights from B and C on the left pan and the weights from D and E on the right pan.

If the result is :

(0) then the heavier balls are not from B, C, D or E. So the two balls in A are the heavier ones.
(1) then the ball B is heavier than all the other ones. This ball and the one left in the box B are the heavier ones.
(2) then the two balls from C are heavier.
(-1) then the ball from D is heavier among the rest. This and the other ball in D are the ones.
(-2) then the two balls from E are the heavier ones.

So the answer is $\boxed 1$ .

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