A box contains a collection of marbles. If you count them by twos, you have one left over. If you count them by threes, you have two left over. If you count them by fours, you have three left over. What is the smallest possible number of marbles in the box?
11
Notice that in every case, the remainder is one less than the divisor (2-1=1, 3-2=1, 4-3=1). This means if you added just 1 marble to the box, the total would be evenly divisible by 2, 3, and 4. The least common multiple of 2, 3, and 4 is 12. Subtracting 1 gives us the smallest possible total of 11 marbles.
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: Medium. More like this: Math riddles with answers or try Target 24 for a different kind of puzzle.
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