### 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?

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.

# Three Fruits

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

Quince, quance, quonce

(1) $7$ quince weigh the same as $4$ quonce, so a quince weighs less than a quonce.

(2) $5$ quonce weigh the same as $6$ quance, so a quance weighs less than a quonce.

So quonce is the heaviest. But $20$ quonce weigh the same as $35$ quince (from (1) multiplied by $5$), and $20$ quonce weigh the same as $24$ quance (from (2) multiplied by $4$), so $35$ quince weigh the same as $24$ quance, so a quance weighs more than a quince.

This problem is taken from the UKMT Mathematical Challenges.
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