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24 (puzzle)

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For short games of 24, once a hand is won, the cards go to the player that won. If everyone gives up, the cards are shuffled back into the deck. The game ends when the deck is exhausted, and the player with the most cards wins.
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Additional operations, such as square root and factorial, allow more possible solutions to the game. For instance, a set of 1,1,1,1 would be impossible to solve with only the five basic operations. However, with the use of
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Longer games of 24 proceed by first dealing the cards out to the players, each of whom contributes to each set of cards exposed. A player who solves a set takes its cards and replenishes their pile, after the fashion of
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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 (
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This article is about the arithmetical puzzle. For the game based on FOX's television series, see
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so that the end result is 24. For example, for the numbers 4, 7, 8, 8, a possible solution is
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The original version of 24 is played with an ordinary deck of playing cards with all the
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is an arithmetical puzzle in which the objective is to find a way to manipulate four
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In a variation of the game played with a standard 52-card deck, there are
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24game.github.io: an online, open-source version of the 24 puzzle
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A slightly different version includes the face cards,
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Some advanced players allow 8: 518:List of all possible solutions to the puzzle 545: 531: 523: 346:{\displaystyle {\tbinom {4+13-1}{4}}=1820} 371: 329: 302: 299: 297: 152: 127:Learn how and when to remove this message 196:{\displaystyle (7-(8\div 8))\times 4=24} 439: 7: 846: 357:Expansion to more complex operations 65:adding citations to reliable sources 861:WikiProject Board & Table Games 856: 882:Card games introduced in the 1960s 448:"Rules of Card Games: Twenty-Four" 307: 25: 206:The problem has been played as a 855: 845: 836: 835: 602: 41: 487:from the original on 2022-03-30 458:from the original on 2022-04-01 52:needs additional citations for 513:General information from Pagat 477:"Facts about 24 the math game" 397: 373: 366:, it is possible to get 24 as 178: 175: 163: 154: 1: 841:Children's card game category 412:{\displaystyle (1+1+1+1)!=24} 851:Children's games at Commons 913: 892:Brain training video games 29: 831: 600: 353:four-card combinations. 262:, and other operations. 897:Card games for children 214:since the 1960s, using 413: 347: 197: 414: 348: 198: 370: 296: 151: 61:improve this article 652:Beggar-my-neighbour 27:Arithmetical puzzle 887:Mathematical games 579:Bohemian Schneider 409: 343: 335: 193: 869: 868: 811:Proprietary games 612:Four-player games 328: 137: 136: 129: 111: 16:(Redirected from 904: 859: 858: 849: 848: 839: 838: 782:Snip-snap-snorum 606: 562:Two-player games 547: 540: 533: 524: 496: 495: 493: 492: 473: 467: 466: 464: 463: 444: 418: 416: 415: 410: 352: 350: 349: 344: 336: 334: 333: 324: 306: 222:Original version 202: 200: 199: 194: 132: 125: 121: 118: 112: 110: 76:"24" puzzle 69: 45: 37: 21: 912: 911: 907: 906: 905: 903: 902: 901: 872: 871: 870: 865: 827: 806: 633: 619:Knock-out whist 607: 598: 557: 551: 504: 499: 490: 488: 475: 474: 470: 461: 459: 446: 445: 441: 437: 425: 368: 367: 359: 308: 301: 294: 293: 224: 149: 148: 133: 122: 116: 113: 70: 68: 58: 46: 35: 28: 23: 22: 15: 12: 11: 5: 910: 908: 900: 899: 894: 889: 884: 874: 873: 867: 866: 864: 863: 853: 843: 832: 829: 828: 826: 825: 820: 814: 812: 808: 807: 805: 804: 799: 794: 789: 784: 779: 774: 769: 764: 759: 754: 749: 744: 739: 734: 729: 724: 719: 717:Jack Change It 714: 709: 707:Happy families 704: 699: 694: 689: 684: 679: 674: 669: 664: 659: 654: 649: 643: 641: 635: 634: 632: 631: 626: 621: 615: 613: 609: 608: 601: 599: 597: 596: 591: 586: 581: 576: 571: 565: 563: 559: 558: 552: 550: 549: 542: 535: 527: 521: 520: 515: 510: 503: 502:External links 500: 498: 497: 468: 438: 436: 433: 432: 431: 424: 421: 408: 405: 402: 399: 396: 393: 390: 387: 384: 381: 378: 375: 358: 355: 342: 339: 332: 327: 323: 320: 317: 314: 311: 305: 252:exponentiation 240:multiplication 223: 220: 192: 189: 186: 183: 180: 177: 174: 171: 168: 165: 162: 159: 156: 135: 134: 49: 47: 40: 26: 24: 14: 13: 10: 9: 6: 4: 3: 2: 909: 898: 895: 893: 890: 888: 885: 883: 880: 879: 877: 862: 854: 852: 844: 842: 834: 833: 830: 824: 823:Woodland Snap 821: 819: 816: 815: 813: 809: 803: 800: 798: 795: 793: 790: 788: 785: 783: 780: 778: 775: 773: 770: 768: 765: 763: 760: 758: 757:Schrum-Schrum 755: 753: 750: 748: 745: 743: 740: 738: 735: 733: 730: 728: 725: 723: 720: 718: 715: 713: 710: 708: 705: 703: 700: 698: 695: 693: 690: 688: 685: 683: 680: 678: 675: 673: 672:Concentration 670: 668: 665: 663: 660: 658: 655: 653: 650: 648: 645: 644: 642: 640: 636: 630: 629:Schrum-Schrum 627: 625: 624:My ship sails 622: 620: 617: 616: 614: 610: 605: 595: 592: 590: 589:Schrum-Schrum 587: 585: 582: 580: 577: 575: 572: 570: 567: 566: 564: 560: 556: 548: 543: 541: 536: 534: 529: 528: 525: 519: 516: 514: 511: 509: 506: 505: 501: 486: 482: 478: 472: 469: 457: 453: 452:www.pagat.com 449: 443: 440: 434: 430: 429:Krypto (game) 427: 426: 422: 420: 406: 403: 400: 394: 391: 388: 385: 382: 379: 376: 365: 356: 354: 340: 337: 325: 321: 318: 315: 312: 309: 290: 288: 284: 280: 275: 273: 267: 263: 261: 257: 253: 249: 245: 241: 237: 233: 229: 221: 219: 217: 216:playing cards 213: 209: 204: 190: 187: 184: 181: 172: 169: 166: 160: 157: 146: 142: 131: 128: 120: 117:December 2015 109: 106: 102: 99: 95: 92: 88: 85: 81: 78: â€“  77: 73: 72:Find sources: 66: 62: 56: 55: 50:This article 48: 44: 39: 38: 33: 19: 797:Vieux Garçon 677:Crazy Eights 584:Russian bank 489:. 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Index

24 Game
24: The Game

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