From one digit

small_unicorn

A number with two identical digits is multiplied by 99. What is the four-digit product if the third digit is 5 ?

from book "The Moscow puzzles" by Boris A. Kordemsky

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Razz

**Posted:** Tue Nov 03, 2009 3:13 pm

$LaTeX$

Guessing and checking gives $99\cdot44=\boxed{4356}$ .

Not sure how to do this without guess and check.

**Posted:** Tue Nov 03, 2009 3:25 pm

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Wallbash Red

DOPE!!! I FAIL AT EVERYTHING!!!
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small_unicorn

**Posted:** Tue Nov 03, 2009 3:29 pm

$LaTeX$

Okay, I found out a non bashy way.

When any number with two identical digits is multiplied by 99, the 1st and 3rd numbers, and the 2nd and 4th numbers, sum to 9. Also, the first digit is one more than the first. From this, we get our number $\boxed{4356}$ .

**Posted:** Tue Nov 03, 2009 3:35 pm

_________________
$I,^{{\LaTeX}^{{Shall}^{{Pwn}^{ALL!}}}}$
Wallbash Red

DOPE!!! I FAIL AT EVERYTHING!!!
I hope this isn't Spam

!!!!! Please rate this post at least a $4$ . If not, please pm me and tell me why.

small_unicorn

**Posted:** Tue Nov 03, 2009 3:57 pm