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Target Number

Two old classroom games that are really one game. You are dealt some numbers and a target, and you have to reach the target using every number exactly once.

The three games

In all three, you combine two numbers at a time with addition, subtraction, multiplication or division. The two become their answer, and you keep going until one number is left. If it is the target, you have it.

24
Four numbers, and the target is always 24. Fractions and negative numbers are allowed on the way, which is what makes the hard ones possible: 3, 3, 8 and 8 only work as 8 ÷ (3 − 8 ÷ 3). The numbers run from 1 to 9, as on the printed cards, or 1 to 13 if you would rather play with a deck of cards.
Krypto
Five numbers and a target, all dealt from the 56-card Krypto deck: three each of 1 to 6, four each of 7 to 10, two each of 11 to 17 and one each of 18 to 25, so small numbers come up most. Every step has to give a whole number, so no fractions and nothing below zero.
Valerie
Three numbers from 1 to 9 and a target from 1 to 12, whole numbers only. The one to start with.

Every puzzle here has at least one answer. Deals that do not are thrown back before you see them, which happens to about one 24 deal in ten and hardly any Krypto deals.