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The original version of 24 is played with an ordinary deck of playing cards with all the face cards removed. The aces are taken to have the value 1 and the basic game proceeds by having 4 cards dealt and the first player that can achieve the number 24 exactly using only allowed operations (addition, subtraction, multiplication, division, and parentheses) wins the hand.
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For example, when d=4, the hash table for two occurrences of d would contain the key-value pair 8 and 4+4, and the one for three occurrences, the key-value pair 2 and (4+4)/4 (strings shown in bold). The task is then reduced to recursively computing these hash tables for increasing n , starting from n=1 and continuing up to e.g. n=4.
The Numbers Game is played twice daily. It draws 4 1-digit numbers, bets can be made on a 1-digit and/or 2-digit number. 3-digit numbers are "first 3" or "last 3," as a 3-digit number is not drawn separately. Minimum wagers are 25 cents on a 3-digit or 4-digit number, and 50 cents on a 2-digit number or 1-digit.
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Therefore, the total number of cards can be reduced by a factor of (5! 4 * 4!) = 4,976,640,000 for a total unique winning card set of 111,007,923,832,370,565 or 111 quadrillion. (Still impossibly enormous, but our eager printer described above would only need 1.29 days to complete the task.)
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Answer: 1 bull and 2 cows. (The bull is "2", the cows are "4" and "1".) The first player to reveal the other's secret number wins the game. The game may also be played by two teams of players, with the team members discussing their strategy before selecting a move. Computer versions of the game started appearing on mainframes in the 1970s.