Make 24

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Numbers and arithmetic operations for Make 24

Make 24 is a math puzzle game . A single player is given the task of generating the result 24 from four single-digit numbers using elementary arithmetic operations.

Rules of the game

The player draws four numbers between 1 and 9 and has to combine them using the basic arithmetic operations to produce the result 24. Only the links +, -, × and / and the use of brackets are permitted. Other arithmetic operations such as powers , roots , faculties etc. are not allowed. It is also not allowed to combine two or three digits to form a multi-digit number.

The drawing of the four numbers can be replaced by another person or a computer program giving the player the task. Make 24 is mostly played with the help of pen and paper. Experienced players solve Make-24 tasks in their heads.

Examples

Given: 6, 8, 9, 9

Solution: 8 × (9 + 9) / 6 = 24

Given: 1, 3, 4, 8

Solution: 4 × (8 - 3 + 1) = 24
Not allowed: 38 - 14 = 24

Make-24 problems are rated as differently difficult by players. The following example seems more difficult than the first two.

Given: 1, 3, 4, 6

Solution: 6 / (1 - 3/4) = 24

Math background

Make 24 is a deduction game and is one of the arithmetic puzzles among the mathematical puzzles . There are possible combinations for the four given numbers . But only 404 of these lead to a solution. 91 have no solution. In many cases the solution is not clear. If the four given numbers are different from one another, there are only possible combinations of which exactly two do not lead to a solution, namely 3, 4, 6, 7 and 1, 6, 7, 8.

Example of an ambiguous solution:

Given: 3, 5, 8, 9

Solutions: 9 × (8 - 5) - 3 = 9 × 3 + 5 - 8 = 24

How many different solutions there are for the individual tasks depends on which solutions are perceived as (essentially) the same. For example, two solutions that are only distinguished by a reversal of the order when adding or multiplying are generally considered to be the same. In contrast, it is not clear whether (7 + 8 + 9) × 1, (7 + 8 + 9) / 1, and 7 + 8 + 9 × 1 are counted as three different solutions. Therefore, in the publications on Make 24, different information on the number of solutions is given. .

Variant of Make 24 with playing cards

Make 24 is also played with playing cards , e.g. B. with a rummy sheet. Four playing cards are drawn at random, the values ​​of which have to be linked to the result 24 according to the usual Make-24 rules. The values ​​of the playing cards 2 to 10 are taken over unchanged, for the 1 the ace is recommended , and for the joker , jack , queen and king values ​​are agreed before the game, e.g. B. 11, 12, 13 and 14.

swell

  1. ↑ a b Frans Reijnhoudt: Solutions to the 24 Game , accessed on September 11, 2009.
  2. ^ Make 24 , accessed September 11, 2009.

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