math
posted by joe .
Members of the West High School Band were hard at work practicing for the annual Homecoming Parade. First, they tried marching in rows of 12, but himself to bring up the rear left Andrew. Then the director told the band members to march in columns of eight, but Andrew was still left to march alone. Even when the band marched in rows of three, Andrew was left out. Finally, in exasperation, Andrew told the hand director that they should march in rows of five in order to have all the rows filled. He was right. Given that there were at least 45 musicians on the field but fewer than 200 musicians. How many students were there in the West High.

Clearly the number must be a multiple of 5, so it could be
45 50 55 60 65 ...145 ... 200
when divided by 12, the remainder is 1, so it could be
49 61 73 85 97 109 121 133 145 .... 193
when divided by 8, the remainder is 1, so it could be
49 57 65 73 81 89 97105 113 121 129 137 145 ...
ahhh, 145 is it!
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