I am the smallest positive integer above 1 that leaves a remainder of 1 when divided by 2, 3, 4, 5, or 6, but leaves no remainder at all when divided by 7. What number am I?
301
The least common multiple of 2, 3, 4, 5, and 6 is 60. The candidate numbers leaving remainder 1 are of the form 60k + 1 (61, 121, 181, 241, 301...). Testing these for divisibility by 7 reveals that 301 / 7 = 43 with zero remainder.
About this riddle
Math riddles hide a calculation inside a short story. Pull out the numbers, work out what is being asked, and watch for a trick such as a unit change.
Difficulty: Hard. More like this: Math riddles with answers or try Target 24 for a different kind of puzzle.
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