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      1 March, 2005
      March 2005

      Racing certainties: solution

      If we discount the favourite (with odds of 1 to 1) and place none of our stake money on him then we are really betting on a three-horse race where Q is equal to Q=14+18+25=3140<1, and by betting 14 of our stake money on runner 1, 18 on runner 2, and 25 on runner 3 we are guaranteed a minimum return of 4031−1= 931 of our total stake in addition to our original stake money!

      In the case of ai=i(i+2)−1 and an infinite number of runners (N=∞) we have Q=∑i=1N1ai+1=∑i=1∞1i(i+2)=34.


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