Saturday, October 27, 2012

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?
 
Puzzle Answer

Answer:

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.
 
 
 

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