### Pebbles

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?

### Happy Numbers

Take any whole number between 1 and 999, add the squares of the digits to get a new number. Make some conjectures about what happens in general.

### Intersecting Circles

Three circles have a maximum of six intersections with each other. What is the maximum number of intersections that a hundred circles could have?

# Weekly Problem 38 - 2009

##### Stage: 3 Short Challenge Level:

The first two terms of a sequence are $\frac{2}{3}$ and $\frac{4}{5}$. Each term after the second term is the mean of the two previous terms. What is the fifth term in the sequence?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.

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