Originally posted by Lord Burn
A farmer is taking her eggs to market in her cart, but she hits a pot-hole, which knocks over all the containers of eggs. Though she herself is unhurt, every egg is broken. So she goes to her insurance agent, who asks how many eggs she had. She says she doesn't know, but she remembers some things from various ways she tried packing the eggs. She ...[text shortened]... r.
What is the smallest number of eggs the farmer had?
Explain how you solved this problem
The given states that the numbers of eggs the woman had is divisible by 2, 3, 4, 5 and 6 rest 1. Since 6 = 2*3 and 4= 2*2 the number has as divisors 2 (two times), 3 and 5.
The smallest number with that property is 2*2*3*5 + 1= 61
Unfortunately this number isn't divisible by 7. The general form of number divisible by 2, 2, 3 and 5 rest 1 is N*2*2*3*5 + 1.
The first few are thus 61, 121, 181, 241 and 301. The smallest of these wich is divisible by 7 is 301.
Thus 301 is the smallest number wich can be written as 2n+1, 3m+1, 4p+1, 5q+1, 6r+1 and 7s. With n, m, p, q, r and s certain positive integers.