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Special Set of Numbers


The numbers {160, 161, 162} constitute a set of 3 consecutive integers that are divisible by 5,7 and 9, respectively.

Find the first set of 4 consecutive integers that are divisible by 5, 7, 9, and 11, respectively.

Answer

The number divisible by 5 had to end in either a 5 or a 0. Therefore, the number divisible by 7 had to end in either a 6 or a 1 and so on. Then starting with a number divisible by 11 (143) I made a list of numbers by adding 55 (198, 253, 308, etc.). Then I proceeded to do the same for 9 starting at 162 and adding 45. When I came across two numbers in sequence I then subtracted one from the lower number and divided it by 7.

{1735,1736,1737,1738}
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