Measure The Strings

You have two strings whose only known property is that when you light one end of either string it takes exactly one hour to burn. The rate at which the strings will burn is completely random and each string is different.

How do you measure 45 minutes?




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When I divide it by 3, the remainder is 2.
When I divide it by 4, the remainder is 3.
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When I divide it by 7, the remainder is 6.
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In 2007, a puzzle was released and $2 million prizes were offered for the first complete solution. The competition ended at noon on 31 December 2010, with no solution being found. Wiki