# [SOLVED] Letter and number substitution problem

• Mar 7th 2008, 02:21 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, 04:07 PM
Soroban
Hello, DINO!

Quote:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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