From: rhinoceros (rhinoceros@freemail.gr)
Date: Sun Feb 29 2004 - 18:59:26 MST
[Rhysenn]
as to the problem of the ten divisions, maybe most of you have figured this out already but if not, 2519 = (5 * 7 * 8 * 9) - 1. I guess you start out with 2*3*4*5*6*7*8*9*10, and then break it down into factors: 2*3*2*2*5*2*3*7*2*2*2*3*3*2*5. Of these factors, leave in only the ones you need to accounts for all the numbers 2-10: 2= the first two, 3= the first three, 4= the first two twos, 5= the five, 6= the first two and three, 7= the seven, 8= the first 3 twos, 9= the first two threes, 10 = the first two and five. Then we end up with 2*3*2*2*5*3*7 = 2520, and subtracting one we have 2519.
[rhinoceros]
Great! Thanks Rhysenn. You saved me at least a couple of hours which I had good reasons to use elsewhere!
So, this calculation works because if we add 1 to the solution it becomes exactly divisible by all these numbers. After finding the number we subtract the 1 that we borrowed.
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