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Arrange the digits 1, 1, 2, 2, 3 and 3 so that between the two 1's there is one digit, between the two 2's there are two digits, and between the two 3's there are three digits.

Day of the Triffids

Stage: 4 Short Challenge Level: Challenge Level:1
Let the number of ivy, nightshade and triffid plants be $i$, $n$ and $t$ respectively.


$2i + 9n + 12t = 120$ 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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