The **24 Game** is an arithmetic card game with the objective to find a way to manipulate four integers so that the final result is 24. For example, for the card with the numbers 4, 7, 8, 8, a possible solution es (7 - (8 ÷ 8)) × 4 = 24. Mental arithmetic and quick thinking are necessary skills for a competitive game.

This is the most important educational game I have experienced. The game comes with many cards. Each card also has a central symbol that denotes its level of difficulty. The goal of the game is to be the first person to touch the card and tell how to make 24 with the four numbers on that card. You can add, subtract, multiply or divide. You must use all four numbers, but use each number only once.

So what makes game 24 transcend traditional memory cards? The game comes with an inherent pressure to be quick with the answers while competing with other kids to be the first to reach a solution. The most important thing is that it has a creative side; Given the four numbers, you can choose how to reach 24 (most cards have more than one way to reach the answer). Knowing that the answer is always 24 relieves the typical math anxiety of getting the correct answer, and instead emphasizes the process and the patterns.

The original version of 24 is played with an ordinary deck of cards with face cards removed. Aces are considered to have a value of 1 and the basic game proceeds with 4 cards dealt and the first player who can reach the number 24 exactly using only the allowed operations (addition, subtraction, multiplication, division and parentheses) wins the hand. Some advanced game modes allow exponentiation, roots, logarithms and other operations.

All players simultaneously uncover their first card. Then they try to calculate "24" using addition, subtraction, multiplication and division (+, -, ÷, ×) with the four cards uncovered.

For **short** games of 24, once a hand is won, the cards go to the player who won. If everyone gives up, the cards are placed back into the deck. The game ends when the deck is exhausted and the player with the most cards wins.

For **longer** games of 24 proceed by distributing the cards to the players first, each of which contributes to each set of exposed cards. A player who solves a set takes his/her cards and returns them to their hand, as in the Card Wars game. Players are eliminated when they no longer have any cards.

Another modality is that when players think they have achieved 24, they puts their hands on the table. They can also put it on the table to deceive other players and make them believe they have the solution. After three players have put their hand, the remaining player must choose one of the three players to give the solution. If the chosen player responds correctly, the remaining player takes the four cards and places them at the bottom of their draw deck. If the chosen player has no solution or answers incorrectly, they must take the four cards and put them in the bottom of their draw deck. The game ends when a player exhausts his draw deck. If no player can find a solution (some combinations of regular cards can not form 24, however the ones here **do** have a solution), everyone can agree to return their respective cards, reorganize them and draw a new card from their draw deck. The game ends when a player exhausts his draw deck.

Use these cards for free. The download contains sets of 4 numbers **with the guarantee that they do have a solution**, they may not be the same as the ones in the commercial game. The red cards are the ones that have less solutions, while the green ones have the most solutions.

These sheets contain small cards to print and cut for free, in a PDF file . Use the password **worksheets.site** to open the PDF.

We did some calculations and think that these are all of the digit combinations that **cannot be used** to form 24, using the four basic operations if you play the game with an ordinary deck of cards:

1111, 1112, 1113, 1114, 1115, 1116, 1117, 1119, 1122, 1123, 1124, 1125, 1126, 1127, 1128, 1129, 1133, 1135, 1137, 1139, 1144, 1145, 1146, 1147, 1148, 1149, 1155, 1156, 1157, 1158, 1159, 1166, 1167, 1168, 1169, 1177, 1178, 1179, 1188, 1189, 1199, 1222, 1223, 1235, 1237, 1245, 1247, 1249, 1255, 1256, 1257, 1258, 1259, 1266, 1267, 1268, 1269, 1277, 1278, 1299, 1345, 1347, 1349, 1355, 1357, 1367, 1369, 1377, 1399, 1446, 1447, 1449, 1455, 1457, 1458, 1459, 1467, 1477, 1479, 1489, 1499, 1556, 1557, 1558, 1559, 1566, 1567, 1568, 1569, 1577, 1578, 1579, 1588, 1589, 1667, 1677, 1678, 1679, 1689, 1699, 1777, 1778, 1779, 1788, 1789, 1889, 1899, 1999, 2222, 2225, 2226, 2229, 2247, 2249, 2256, 2257, 2267, 2269, 2277, 2279, 2299, 2334, 2346, 2357, 2446, 2447, 2459, 2467, 2469, 2477, 2479, 2499, 2555, 2556, 2559, 2566, 2577, 2578, 2579, 2589, 2599, 2666, 2667, 2668, 2669, 2677, 2678, 2679, 2688, 2689, 2777, 2778, 2779, 2788, 2789, 2799, 2888, 2899, 2999, 3335, 3338, 3347, 3348, 3349, 3355, 3358, 3379, 3388, 3455, 3457, 3459, 3467, 3478, 3488, 3555, 3556, 3558, 3567, 3577, 3578, 3599, 3667, 3668, 3677, 3678, 3679, 3777, 3778, 3779, 3788, 3799, 3888, 3889, 3899, 3999, 4445, 4449, 4477, 4489, 4499, 4556, 4557, 4558, 4559, 4566, 4567, 4568, 4569, 4577, 4578, 4579, 4588, 4589, 4599, 4667, 4668, 4669, 4677, 4699, 4777, 4778, 4779, 4789, 4799, 4888, 4889, 4899, 4999, 5556, 5557, 5558, 5567, 5569, 5577, 5578, 5579, 5599, 5666, 5667, 5668, 5669, 5677, 5678, 5689, 5699, 5777, 5789, 5799, 5889, 5899, 6667, 6677, 6679, 6689, 6699, 6778, 6779, 6789, 6799, 6899, 6999, 7779, 7788, 7789, 7899, 7999, 8899, 8999