Find the Unique Number

Can you find the least possible number such that

If the number is divided by 3, it gives the remainder of 1;
If the number is divided by 4, it gives the remainder of 2;
If the number is divided by 5, it gives the remainder of 3;
If the number is divided by 6, it gives the remainder of 4.




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Teaser Puzzle

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In an office's desk, you find a unique method that shows the current day of the month. Two numbered cubes are used to depict the current date.

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