### Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

### Tea Cups

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

### Counting on Letters

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?

# Fly Away

##### Stage: 3 and 4 Short Challenge Level:

$a=2$, $f=8$, $l=7$, $w=6$ and $y=5$.

We note first that $y=5$ since that is the only non-zero digit that, when it is multiplied by 3, has itself as the units digit. So there is a carry of 1 into the tens column. We note also that $a=1$ or $a=2$ as "$fly$"$< 1000$ and therefore $3\times$ "$fly$"$< 3000$. We now need $3\times l+1$ to end in either 1 or 2 and the only possibility is $l=7$, giving $a=2$ with a carry of 2 into the hundreds column. As $a=2$, $f$ must be at least 6. However, if $f=6$ then $w=0$ which is not allowed. Also, the letters represent different digits, so $f\neq 7$ and we can also deduce that $f\neq9$ since $f=9$ would make $w=9$. Hence $f=8$, making $w=6$ and the letters represent $875\times 3=2625$.

This problem is taken from the UKMT Mathematical Challenges.
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