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An old egg problem (Posted on 2019-11-05) Difficulty: 2 of 5
An old woman went to the market and a horse stepped on her basket and smashed her eggs. The rider offered to pay for the eggs and asked her how many there were. She did not remember the exact number, but when she had taken them two at a time there was one egg left, and the same happened when she took three, four, five, and six at a time. But when she took them seven at a time, they came out even. What is the smallest number of eggs she could have had?

No Solution Yet Submitted by Danish Ahmed Khan    
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more formally | Comment 3 of 5 |
Yes - it's 301. 

I just wanted to write it formally. 

We look for the LCM (least common multiple) of 3,4,5,6 - times some number, that when 1 is added is a multiple of 7. The LCM is 2^2x3x5=60 
So we mult 60 by 2,3,4,5,6, (not 7), 8, etc. and add 1 until we get a multiple 7.
5 does it. so, 301. 

Likely there is a more formal way so we don't even have to guess "5".




  Posted by Steven Lord on 2019-11-05 09:06:09
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