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Las Vegas Casinos

 To avoid competing with one another, five top poker players decide to play poker at different casinos in Las Vegas. The will choose different card games and agree to gamble limited amounts of money. This is the procedure the poker players agree upon  Michael M divides the cards into three piles: 6 Casino cards, 6 Games cards, 9 Cash cards. He picks randomly one card from the casino pile , one card from the games stack, and one card from the cash pile. He sets aside these three cards which become the "mysterious combination". Michael M then shuffles the remaining 18 cards and deals three cards to each player. At various times in the game, a player may suggest a combination of casino, game and cash as a solution to the "mysterious combination". After such a suggestion, each player to the left in turn either passes (indicating that he or she does not hold any of the three cards in the suggestion) or disproves the suggestion (indicating. that he or she does hold at least one of the three cards). As soon as someone has disproved the suggestion, the turn is over. The  players follow the curious house rule that if anyone is dealt a hand of three cards of the same type (three casinos, three games, or three cash) at the beginning of the game, he or she has to announce it. After 16 suggestions have been made and disproved, the players (who were not very good at logical thinking) didn't realize that there was enough information to solve the mystery. Note: It is possible that, for deceptive purposes, a player might hold one or more of the cards in his or her own suggestion. Hints: 1. When Phil  suggested that the mysterious combination was the Bellagio playing Texas Hold'em Poker with  \$7000, Vanessa  (having none of those three cards) passed, and Tom  (having at least one of those three cards) disproved it. 2. When Vanessa  suggested that the secret combination was the Bellagio, playing Crazy Pineapple Poker with \$6000, Tom  and Annette  passed.  Then, before Jonathan could say anything, Michael passed. Jonathan scolded Michael  for speaking out of turn, and said he could disprove the suggestion himself, but it didn't occur to any of the players to make use of the information Michael had glven away. 3.When Jonathan suggested that the mysterious combination was the MGM Grand playing Texas Hold'em Poker with \$4000, Michael passed and Phil disproved it. 4. When Michael suggested that the mysterious combination was Ceasar's Palace playing Old Maid with \$5000, Phil  disproved it. 5. When Phil  suggested that the mysterioous combination was the Luxor playing Crazy Pineapple Poker with \$9000, Vanessa passed and Tom disproved it. 6. When Vanessa suggested that the mysrerious combination was the MGM Grand playing Omaha High with \$9000, Tom, Annette and Jonathan  passed. Michael disproved it. 7. When Tom suggested that the secret trio was by Mandalay Bay playing Old Maid with \$8000, Annette, Jonathan, and Michael  passed, and Phil disproved it. 8. When Annette suggested that the combination was the Luxor playing Razz Poker with \$3000, Jonathan disproved it. 9. When Jonathan suggested that the mysterious combination  was the Bellagio playing Crazy Pinapple Poker with \$5000, Michael passed, and Phil disproved it. 10. When Phil suggested that the mysterious combination was the Mandalay Bay playing Texas Hold'em Poker with \$2000, Vanesssa disproved it, 11. When Vanessa suggested that the mysterious trio was Ceasar's Palace playing Seven Card Stud with \$7000, Tom  passed, and Annette disproved it. 12. When Tom suggested that the mysterious combination was Ceasar's Palace  playing Razz Poker with \$8000, Annette, Jonathan, Michael and Phil passed, and Vanessa disproved it. 13. When Annette  suggested that the mysterious trio was the Bellagio playing Old Maid with \$7000, Jonathan,  Michael passed, and Phil disproved it. 14. When Michael suggested that the combination trio was the Luxor playing Seven Card Stud Poker with \$4000, Phil  disproved it. 15. When Phil suggested that the mysterious combination trio was the Mirage playing Seven Card Stud Poker with \$1000 Vanessa disproved it. 16. When Vanessa suggeited that the mysterious combination was the Mirage playing Omaha High with \$3000, Tom  disproved it. Question : Can you identify the three cards in each player's hand? Can you determine which casino, game, and cash cards were not held by anyone and were therefore the solution to the mysterious combination? See answer
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