Problem solving question

**HerroDere** · April 30th 2012, 12:53 AM

Hi guys, I am at a loss when it comes to these questions, so I was wondering if somebody would help me out.

Identify the numbers represented by letters.
P, Q, R are all different numbers and not zero.
QP0 x
PQR
3RR0 +
49Q00
QP000
P242R0

**Soroban** · May 2nd 2012, 01:16 PM

Hello, HerroDere!

This is called an "Alphametic".

$\text{Identify the digits represented by letters. }\;P, Q, R\text{ are different nonzero digits.}$

. . $\begin{array}{ccccccc} ^1 & ^2 & ^3 & ^4 & ^5 & ^6 \\ &&& Q & P & 0 \\ && \times & P & Q & R \\ \hline && 3 & R & R & 0 \\ & 4 & 9 & Q & 0 \\ & Q & P & 0 \\ \hline P & 2 & 4 & 2 & R & 0 \end{array}$

In column-1, we see that $P = 1.$

$\text{We have: }\;\begin{array}{ccccccc} ^1 & ^2 & ^3 & ^4 & ^5 & ^6 \\ &&& Q & 1 & 0 \\ && \times & 1 & Q & R \\ \hline && 3 & R & R & 0 \\ & 4 & 9 & Q & 0 \\ & Q & 1 & 0 \\ \hline 1 & 2 & 4 & 2 & R & 0 \end{array}$

In column-3, we see that the sum is 14.
Hence, column-2 is: . $4 + Q + 1 \:=\:12 \quad\Rightarrow\quad Q = 7$

$\text{We have: }\;\begin{array}{ccccccc} ^1 & ^2 & ^3 & ^4 & ^5 & ^6 \\ &&& 7 & 1 & 0 \\ && \times & 1 & 7 & R \\ \hline && 3 & R & R & 0 \\ & 4 & 9 & 7 & 0 \\ & 7 & 1 & 0 \\ \hline 1 & 2 & 4 & 2 & R & 0 \end{array}$

In column-4: . $R + 7 \,=\,12 \quad\Rightarrow\quad R \,=\,5$

$\text{Therefore: }\;\begin{array}{ccccccc} ^1 & ^2 & ^3 & ^4 & ^5 & ^6 \\ &&& 7 & 1 & 0 \\ && \times & 1 & 7 & 5 \\ \hline && 3 & 5 & 5 & 0 \\ & 4 & 9 & 7 & 0 \\ & 7 & 1 & 0 \\ \hline 1 & 2 & 4 & 2 &7 & 0 \end{array}$

**HerroDere** · May 11th 2012, 03:10 AM

thanks for that

your explanation really helped

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