The band director was having a terrible time lining up his high school band for the Thanksgiving Day Parade. He didn’t have all that many kids, fewer than one hundred, but he couldn’t seem to arrange them on parade properly. He kept having odd numbers left over. He tried rows of five and there were four left over; he tried rows of six—four left over; rows of seven —one left over. He finally decided to have a very narrow parade and arranged them four abreast. That worked. What’s the smallest number of band members he could have had?
Edit: Come on people... show how you got there anyway.
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magicmarmot- Tom Ramcigam
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5x+4 = 6y+4 = 7z+1 = 4w
Line it up in a matrix, and it's pretty easy to figure out.
Otherwise, if you just look at 5x+4 = 6y+4, it's easy to see that x is a multiple of 6. x=6 gives 34 as an answer, which doesn't add up. x=12, though, yields 64, which works.
Shorter would have been to figure out the 5 and 6 multiples (30, 60, 90) then add 4 to see which one has a multiple of 7 near it.
If it's rows of six, then it's 34, 64 or 94.
And rows of seven limits it to 64.