Jasmine spends exactly £120 on three types of plants: poisoned ivy, deadly nightshade and triffids.

Poisoned ivy plants cost £2 each, deadly nightshade plants cost £9 each and triffids cost £12 each.

She buys twenty plants in total, including at least one of each type. How many triffids did she buy?

This problem is taken from the UKMT Intermediate Mathematical Challenges.