Thursday, July 06, 2006

The matches

Ah, my friend... long time no Perelman? Suffer no more, here is the next problem for you.

You have 48 matches in 3 groups. From the first group, you move to the second as many matches are in the second. Then, from the second group you move to the third as many matches are in the third. Then, from the third group, you move to the first as many matches are in the first. At this point, all groups have the same amount of matches. How many matches were in each group to begin with?

2 comments:

Anonymous said...

I ended up with 22, 14, and 12 for the three groups. I worked the problem backwards from 3 groups of 16.

Andres said...

Correct!

When I first read the problem, I felt a bit surprised --- "and a solution to this is possible in integers?... wow".