# Puzzle page

Issue 54
in
March 2010

## Eggstreme division

Image by Sister72

Awash with chocolate eggs and gift bags, confectionery delirium sets in and your mind starts to wander... Given you have 20 bags, what is the minimum number of eggs needed so that you have a different number of eggs in each bag? (And here's a hint: go against common sense and try putting all your eggs in one basket!)

This puzzle was taken from the regular Puzzle Corner column for the Gazette of the Australian Mathematical Society. Why not try your hand at the problems in the latest Puzzle Corner?

If you are stumped by last issue's puzzle, here is the solution.

For some challenging mathematical puzzles, see the NRICH puzzles from this month or last month.

### Thinking differently

Put one egg in each bag except one
Put the empty bag in an egged bag
Put that bag in an egged bag
This way, you only use 19 eggs, but the top bag has 0 eggs, the next has one, the next has 2 etc
(Yes, this is a bit cheaty, but it said go against common sense :P )

99

### if you don't put all eggs in

if you don't put all eggs in one basket

0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 = 190 eggs

or

put one egg in 19 bags...
put the first bag (withought an egg) in the second bag in the third, etc.

so... 19