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Counting Factors

Is there an efficient way to work out how many factors a large number has?

Summing Consecutive Numbers

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

Oh! Hidden Inside?

Find the number which has 8 divisors, such that the product of the divisors is 331776.

Water Lilies

Age 11 to 14 Challenge Level:

water lilies

There are some water lilies in a lake.

The area that they cover doubles in size every day.

After 17 days the whole lake is covered with water lilies.

How long did it take them to cover half the lake?