Three darts, a board of numbers and a target total. You may hit the same value more than once, but you must use exactly three valid throws. Our interactive Darts game offers 36 challenges: the first have just one combination; later you must find every possibility.
The rule that changes everything
A combination does not depend on throw order. For example, 7 + 11 + 24 and 24 + 7 + 11 are the same answer. On the other hand, 4 + 4 + 32 is allowed: you can hit 4 twice. Reaching the target with two darts or four is not enough.
A method beyond guessing
Mentally sort the available values. Choose a first value a, then seek two values b and c whose sum is the target minus a. To avoid counting the same combination repeatedly, require a ≤ b ≤ c. Rejecting remainders that are too small or too large makes the search both quick and complete.
An example: 42 points
The first board contains 1, 4, 7, 8, 11, 13 and 24. The target of 42 is reached by 7 + 11 + 24. If you choose 24 first, 18 points remain: 7 + 11 = 18. The game checks the sum automatically and remembers the combinations you have found.
A small editorial correction
Puzzle 10 in the photographed page says “64 points”, but its printed solution is 4 + 4 + 32 = 40. Moreover, 64 points would yield two combinations, contrary to the book's statement that the first 24 puzzles have unique solutions. The game therefore uses 40 points and makes this choice explicit.
Source
The number-board configurations are adapted from “Freccette” in Numeri by Dario De Toffoli, Dario Zaccariotto and Silvia De Toffoli, Hachette, pp. 227–236. The digital board, interaction and explanations are an original adaptation; they do not reproduce photographs of the pages.