| The Diophantine Dog House - Answer |
| Wednesday, 04 October 2006 | |
Answer:Calling the number of dogs in the house a, the number of dogs in the kennels before yesterday n, and the number of dogs in total now m, we can derive the following equations: n = 4a + 2 and m = 4/3 n + a Therefore: 3m = 4n + 3a Substituting n with 4a + 2: 3m = 19a + 8 This is a Diophantine equation, hence the name of the problem. This equation has an infinite number of discrete solutions becausedue to the fact that m and a must be whole numbers. For example, m = 9 and a = 1 is a possible solution to the equation. However, not all of the solutions will fit the problem because we know that a is greater than 7 and that m is less than 50fifty. The only solution which fits these conditions is m = 47 and a = 7. That’s a lot of dogs! |
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