# Hint to Riddle #24: The Market

24. You're a farmer. You're going to a market to buy some animals. On the market there are 3 types of animals for sale. You can buy: Horses for £10 each, goats for £1 each and ducks, you get 8 of these per bunch and each bunch costs £1. The aim is to acquire 100 animals at the cost of £100, what is the combination of horses, goats and duck that allows you to do this? (you must buy at least one of each.)

You can just brute force this, just try lots of combinations until you get to the right one. There are certain criteria in the puzzle that mean we can make sort of sensible choices.

But there is no fun in that. To 'solve' the puzzles we need to use ruthless logic and start building equations for example H + G + D = 100 (animals).

There are only two equations we can use though and three variables that we are trying to solve for. But as we get nearer the end other things, like you can only buy integer horses will cause the solution to appear.

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