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| Curious Consecutive Cyphers (Posted on 2008-11-25) |
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Each of the last T digits in the decimal representation of the product of 1!*2!*3!.....99!*100! is zero, but the (T+1)th digit from the right is nonzero.
Determine the remainder when T is divided by 1000.
Note: Try to derive a non computer-assisted method, although computer program/spreadsheet solutions are welcome.
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Submitted by K Sengupta
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Rating: 2.0000 (1 votes)
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Solution:
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The required remainder is 124.
For an explanation, refer to the respective solutions submitted by:
(i) Steve Herman in this location.
(ii) Dej Mar in this location.
(iii) Charlie in this location which also gives the full expansion of 100!
(iv) Ady TZIDON in this location.
Dej Mar and Charlie has extended the problem by way of determining the Tth+1 digit from the right, here and here.
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