Find the lowest number that has a remainder of(adsbygoogle = window.adsbygoogle || []).push({});

1 when divided by 2,

2 when divided by 3,

3 when divided by 4,

4 when divided by 5, and

5 when divided by 6.

It is possible to solve this by applying the general algorithm that solves Chinese Remainder problems. But, for this special case of the CRT, there is an much quicker way. You just have to look at it right and the answer pops out. ....

Naturally, the point of this problem is more about finding the trick than it is about finding the right answer.

Hints:

6=3x2 and 4 = 2x2.

Problem Source:

Problem 35 on p. 11 in Chp. 1 of Carter and Russell, "The Complete Book of Fun Maths"

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# The Chinese Remainder Theorem (the CRT)

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