Enigma 1265: Going to the dogs
7 January 2015
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From New Scientist #2421, 15th November 2003 [link]
George was celebrating the fact that on a charity night at his local greyhound track there was no betting tax and the bookmakers’ odds precisely reflected the amounts staked on each dog.
In the first race, the quoted odds-to-one-against each of the six dogs were all different prime numbers. George placed a bet on each dog – £1 on the outsider, higher integer amounts on the others. He then calculated that, irrespective of which dog won, his winnings (including the return of his winning stake) would equal the total amount he staked.
While he was thinking this was a rather pointless exercise, the dog in Trap-1 was withdrawn. George then calculated that if all the bets on that dog (including his) were transferred to the dog in Trap-2, and the odds recalculated accordingly, the odds-to-one-against the five runners would still be different integers.
If this happened, what would be the revised odds for the dog in Trap-2?