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#131 The Paradise Club

Down at The Paradise Club, Gus and Bart take it in turns to roll a pair of dice. The first person to score his favourite score for two dice wins, which means being treated to a drink by the other (the loser). They each favour a different prime number as a score with two dice and it so happens that their chances of getting their favourite score is the same for each.

What is that probability? If Gus goes first what are his chances of being bought a drink?

Solution next week

#130 Arithmagic

Solution

Reading down the columns, the three sets of five deletions are as follows: 83229, 25743 and 96696. The quickest route to the solution is to look at the subtraction in the last three rows.

If you try different ways of removing a digit from each row, the only combination that leads to a correct subtraction is 675 鈥� 349 = 326. The first two rows therefore add to 675, and can only be 219+456=675. The next set of removed digits leaves 19 + 46 = 65, and 65 鈥� 39 = 26, and finally 1 + 4 = 5 and 5 鈥� 3 = 2.