By Stephen P. Richards
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Extra resources for A Number for Your Thoughts
Does the '3' row stay ahead for long, or perhaps forever? I will not spoil the fun by telling you the answer at the N = 1000 marker - you can place your wagers and then find out for yourself by using the prime number table in Chapter 2. As far as the infinite limit is concerned, it has been shown theoretically that each row leads infinitely often so that the race itself can never be said to be won outright by either side. At any finite 'distance post', on the other hand, the race does have a leader (or is tied) and the competition is keen.
R. Kaprekar started to play with integers in a new and rather fascinating way. It was really a type of solitaire game in the beginning, and the rules are simple enough for anyone to play. In the era of the pocket calculator the procedure is not even particularly time consuming, and the moves of the game are as follows: a) Think of an integer which contains more than one digit. b) Arrange the digits in decreasing numerical order so as to make the largest number possible out of them (not all the digits must necessarily be different but they should not all be the same).
These numbers are 099, 198, 297, 396, 495, 594,693, 792, 891. After these have been arranged with their digits in decreasing numerical order to start the second subtraction routine, we 'are left with only five numbers (990, 981, 972, 963, and 954) which need to be tested further. It is now a simple process to check out these five in detail - in fact, all except 990 already appear in our example above - and confirm the unique property of 495 as the self-reproducing endpoint for all 3digit numbers.