Difference between revisions of "Talk:Broken Eggs POW"
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:I gather that you were still a schoolboy when you cracked this one, and that you didn't know about modulo arithmetic. Congratulations on getting there the hard way. | :I gather that you were still a schoolboy when you cracked this one, and that you didn't know about modulo arithmetic. Congratulations on getting there the hard way. | ||
| − | :The easy way is : begin by finding the Least Common Multiple of 2,3,4,5,6, which is 60. | + | :The easy way is : begin by finding the Least Common Multiple of 2,3,4,5,6, which is 60. Then ( 60n +1 ) will have remainder 1 when divided by 2,3,4,5 or 6 (60/7) mod 7 is 4 so (60n/7 +1) mod 7 = (4n+1) mod 7. Simply try n= 1,2,3,4,5,6,7 . You will see that for n = 5, (4n+1) = 21 which is 0 mod 7. so eggs are 5.60 +1. Adding 7 to n (or adding 420 to previous answer) will always produce a good new solution. Thanks again for the info. Best regards tpm |
| − | Then ( 60n +1 ) will have remainder 1 when divided by 2,3,4,5 or 6 | + | |
| − | (60/7) mod 7 is 4 so (60n/7 +1) mod 7 = (4n+1) mod 7. Simply try n= 1,2,3,4,5,6,7 . | + | |
| − | You will see that for n = 5, (4n+1) = 21 which is 0 mod 7. so eggs are 5.60 +1. | + | |
| − | Adding 7 to n (or adding 420 to previous answer) will always produce a good new solution. | + | |
| − | Thanks again for the info. Best regards tpm | + | |
Latest revision as of 18:03, 18 January 2009
this problem is trivial to a number theorist, straight-forward to anyone who uses (or has studied) modulo arithmetic, and a bit challenging to anyone else unless they do it by trial and error.The general solution of course is 301+420n for n= 0, 1, 2, . . . of which the smallest is 301. cheers tpm
- I gather that you were still a schoolboy when you cracked this one, and that you didn't know about modulo arithmetic. Congratulations on getting there the hard way.
- The easy way is : begin by finding the Least Common Multiple of 2,3,4,5,6, which is 60. Then ( 60n +1 ) will have remainder 1 when divided by 2,3,4,5 or 6 (60/7) mod 7 is 4 so (60n/7 +1) mod 7 = (4n+1) mod 7. Simply try n= 1,2,3,4,5,6,7 . You will see that for n = 5, (4n+1) = 21 which is 0 mod 7. so eggs are 5.60 +1. Adding 7 to n (or adding 420 to previous answer) will always produce a good new solution. Thanks again for the info. Best regards tpm
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