Russian mathematics olympiad question

[aero_dude]

Hello!

The following question was asked in a Soviet Union mathematics Olympiad about 2-3 decades ago. A friend brought it up a few days ago and it has been bugging us since then.

The problem goes along the lines of:

"There are 10 ammo boxes each containing 10 bullets, and each bullet weighs 10 grams.
However, one of the boxes contains defective bullets which weigh 9.9 grams each. Being allowed to use a scale only ONCE, find the ammo box containing the defective bullets"

- The scale is not a balance scale
- One use of scale refers to one reading

This is more of a logic problem then mathematical, but as I said it was in the math competition.

 

[Ronankeating]

You should get bullet collection where the sequence of bullets is important, for example from the 1st box pick one bullet, from 2nd box pick two bullets, from 3rd box pick 3 bullets... from 10th box pick 10 bullets. So totally you get 10*11/2=55 bullets collection, that means it should be 55*10gr = 550gr in total. You put all of this bullets collection(55 in scale to measure and if you get 549.7 gr that means 0.3 gr is missing and 3rd box where discrepancy occurs, and if it's 549.6 that means 0.4gr missing and 4th box and so on ..