# [SOLVED] Letter and number substitution problem

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• Mar 7th 2008, 03:21 PM
DINO
[SOLVED] Letter and number substitution problem
Need help I am a parent of a Yr 8 student and she has asked me to help her with Maths problem. I cant do it!

Problem

Each letter stands for a different digit. If WAIT = 8472,what does STOP represent.

Given that

GO
+SLOW
---------
STOP

Any help would be appreciated.
Thanks(Talking)
• Mar 7th 2008, 05:07 PM
Soroban
Hello, DINO!

Quote:

Each letter stands for a different digit.
If $WAIT = 8472$, what does $STOP$ represent?

$\begin{array}{ccccc} & & G & \Theta \\
S & L & \Theta & W \\ \hline
S & T & \Theta & P \end{array}$

We given: . $W=8,\;A=4,\;I=7,\;T=2$
. . Available digits: . $\{0,1,3,5,6,9\}$

. . $\begin{array}{ccccc} ^1 & ^2 & ^3 & ^4 \\
& & G & \Theta \\
S & L & \Theta & {\bf{\color{blue}8}} \\ \hline
S & {\bf{\color{blue}2}} & \Theta & P \end{array}$

In column-3: $G + \Theta$ ends in $\Theta$

$G$ could be $0$ (zero).
Then there would be no "carry" to column-2 and $L = 2.$
Since $T = 2$, this is not possible.

Hence, $G = 9$ and $L = 1.$
. . And there is a "carry" from column-4.

. . $\begin{array}{ccccc} ^1 & ^2 & ^3 & ^4 \\
& & {\bf{\color{blue}9}} & \Theta \\
S & {\bf{\color{blue}1}} & \Theta & {\color{blue}8} \\ \hline
S & {\color{blue}2} & \Theta & P \end{array}$

Available digits: . $\{0,3,5,6\}$

In column-4: $\Theta + 8$ ends in $P.$
The only combination is: . $\Theta = 5,\,P=3$

. . $\begin{array}{ccccc} ^1 & ^2 & ^3 & ^4 \\
& & {\color{blue}9} & {\bf{\color{blue}5}} \\
S & {\color{blue}1} & {\bf{\color{blue}5}} & {\color{blue}8} \\ \hline
S & {\color{blue}2} & {\bf{\color{blue}5}} & {\bf{\color{blue}3}} \end{array}$

Available digits: . $\{0,6\}$

It assumed that a number will not begin with zero.
. . Hence: . $S = 6$

. . $\begin{array}{ccccc} & & {\color{blue}9} & {\color{blue}5} \\
{\bf{\color{blue}6}} & {\color{blue}1} & {\color{blue}5} & {\color{blue}8} \\ \hline
{\bf{\color{blue}6}} & {\color{blue}2} & {\color{blue}5} & {\color{blue}3} \end{array}$

Therefore: . $S\,T\,O\,P = 6\,2\,5\,3$