### 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?

### It Figures

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

### Bracelets

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

# Weekly Problem 35 - 2011

##### Stage: 2 and 3 Short Challenge Level:

Find the number:

it's less than $100$;
it's one more than a multiple of $3$;
exactly one of its digits, you get a prime;
if you reverse its digits, you get a prime;
it has exactly four factors;
the sum of its digits is prime;
if you multiply it by $5$, the answer is greater than $100$.

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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