### Domino Square

Use the 'double-3 down' dominoes to make a square so that each side has eight dots.

### 4 Dom

Use these four dominoes to make a square that has the same number of dots on each side.

### Pair Sums

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

# Weekly Problem 23 - 2013

##### Stage: 3 Challenge Level:
Let the number of ivy, nightshade and triffid plants be $i$, $n$ and $t$ respectively.

Then:

$2i + 9n + 12t = 120$ and $i + n+ t = 20$, where $i> 0$; $n> 0$; $t> 0$.

Multiplying the second equation by $2$ and subtracting the new equation from the first:
$$7n + 10t=80$$
Thus $$7n = 10(8-t)$$
Therefore $n$ is a multiple of $10$ and since 1 \le n < 20 , $n=10$

Hence $8-t=7$ and therefore $t=1$.

This problem is taken from the UKMT Mathematical Challenges.

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