Find a number
A number with an interesting property:
When I divide it by 2, the remainder is 1. When I divide it by 3, the remainder is 2. When I divide it by 4, the remainder is 3. When I divide it by 5, the remainder is 4. When I divide it by 6, the remainder is 5. When I divide it by 7, the remainder is 6. When I divide it by 8, the remainder is 7. When I divide it by 9, the remainder is 8. When I divide it by 10, the remainder is 9.
It's not a small number, but it's not really big, either. When I looked for a smaller number with this property I couldn't find one.
Can you find it?
The answer is 2519.
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1 solution
Find the LCM of 2,3,4,5,6,7,8,9,10. It is 2520.
Number is: 2520-1 = 2519
Other approach
The number has to end in 9. Look brute force for small numbers. 39 + multiples of 40, 69 + multiples of 70 and 89 + multiples of 90 Smallest one is 2519.