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Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

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Adding All Nine

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some other possibilities for yourself!

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Have You Got It?

Can you explain the strategy for winning this game with any target?

Essential Supplies

Stage: 3 Short Challenge Level: Challenge Level:1

2005/12 = 167 remainder 1.
So, if 167 of the larger boxes are used 1 bar will remain.

It follows that if 166 larger boxes are used there will13 bars left (not a mulitple of 5).
However, if 165 of the larger boxes are used this will leave 25 bars, which can be packed into 5 of the smaller boxes.

Total number of boxes is 165 + 5 = 170.

This problem is taken from the UKMT Mathematical Challenges.