### Double Digit

Choose two digits and arrange them to make two double-digit numbers. Now add your double-digit numbers. Now add your single digit numbers. Divide your double-digit answer by your single-digit answer. Try lots of examples. What happens? Can you explain it?

### Pyramids

What are the missing numbers in the pyramids?

### Mindreader

A little bit of algebra explains this 'magic'. Ask a friend to pick 3 consecutive numbers and to tell you a multiple of 3. Then ask them to add the four numbers and multiply by 67, and to tell you the last two digits of her answer. Now you can really amaze her by giving the whole answer and the three consecutive numbers used at the start.

# Age of Augustus

##### Stage: 3 Short Challenge Level:
The square numbers around $1871$ are $42^2=1764$, $43^2=1849$ and $44^2=1936$. The only realistic possibility is that de Morgan was $43$ in the year $1849$, which puts his date of birth at $1806$.

This problem is taken from the UKMT Mathematical Challenges.
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