Talk:Broken Eggs POW - Revision history

ThePlaz at 18:03, 18 January 2009

2009-01-18T18:03:33Z

ThePlaz: fix formatting

2009-01-18T18:03:07Z

fix formatting

ThePlaz: add new communications from tpm

2009-01-18T18:02:27Z

add new communications from tpm

ThePlaz: post an email I got

2009-01-16T13:58:23Z

post an email I got

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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

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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.
-: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

@@ Line 2: / Line 2: @@
 :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 .

← Older revision		Revision as of 18:02, 18 January 2009
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	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		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