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The tens digit (Posted on 2025-05-12) Difficulty: 2 of 5
(1012-1002)(1022-1012)(1032-1022)...(2002- 1992)

Determine the tens digit of the number above.

No Solution Yet Submitted by Danish Ahmed Khan    
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Solution Solution Comment 1 of 1
The product could have been written as
201*203*205*...*399
and since we only need the last two digits
(1*3*5*...*99)*(1*3*5*...*99)
In each of the parentheses, since there is a factor of 5 and all odd numbers, the last digit will be 5.  Also since there is a factor of 25, the last two digits will be either 25 or 75.

ach of the parentheses are the same so it does matter which:  25^2 and 75^2 both end in 25

The tens digit is 2.




  Posted by Jer on 2025-05-12 07:52:42
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