An old woman goes to a market, and a horse steps on her basket and crushes the e

Question

An old woman goes to a market, and a horse steps on her basket and crushes the eggs. the rider offers to pay for the damages and asks her how many eggs she had bought. She doesnt remember the exact number, but when she had taken them out two at a time, there was one egg left. The same happened when she picked them out three, four, five and six at a time, but when she took them out seven at a time, they came out even. What is the smallest number of eggs she could have had?
.... I know that the answer is 91 and they some how got it by 7*13 = 91 , 91-1 is sivisible by 2 3 4 5 and 6 .... but i dont know how they got 7*13

Explanation / Answer

there are 301 eggs. think about it using a table using mods n amt taken out b remainder ab (mod n) n|a-b 2 1 x1 (mod 2) 2|a-1 3 1 x1 (mod 3) 3|a-1 4 1 x1 (mod 4) 4|a-1 5 1 x1 (mod 5) 5|a-1 6 1 x1 (mod 6) 6|a-1 7 0 x0 (mod 7) 7|a now you need to think what number minus 1 is divisible by 6,5,4,3 and 2 and that number is also divisible by 7. if you do some guess and check you will get 301.

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