Math Problem: "SEND MORE MONEY"
yj...@pacific.net.sg
I am faced with the following algebra problem:
SEND
MORE
+____
MONEY
The question says to make SEND plus MORE = MONEY. I am supposed to fill
in a number from 1 to 9 for each letter. How can I solve this? I need a
reply urgently, I have to hand up my report in two days' time. Thanks!
Yang Jun
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Mike Housky
yj...@pacific.net.sg wrote:
>
> I am faced with the following algebra problem:
>
> SEND
> MORE
> +____
> MONEY
>
> The question says to make SEND plus MORE = MONEY. I am supposed to fill
> in a number from 1 to 9 for each letter. How can I solve this? I need a
> reply urgently, I have to hand up my report in two days' time. Thanks!
There's more than that. All occurrances of a given letter stand for the
same digit. Two different letters always stand for different digits. (Can
you tell that this is a rather famous puzzle? :o) This style of puzzle is
called a cryptarithm and was invented by Henry Ernest Dudeny in the late
19th century.
You can get close enough with a knowledge of decimal arithmetic so that
there are only a few cases to examine by trial and error. Here is an
example of the type of reasoning used to solve cryptaritms. First a few
preliminaries. In a two-line "column" addition, the largest single-
column sum that can be produced is 19 = 9 + 9 + 1, where the 1 is a carry
from the column to the right. The carry is at most 1. I'll use the
letter c to stand for a possible carry, either 0 or 1.
First, neither S nor M is 0, since leading zeros are not written. Second,
M in MONEY is the carry from the S+M+c to the right--so M=1. Next, note
S+M+c=S+0+c is at least 10 (it produced a carry) but at most 11. So,
0=0 or O=1. However 1 is taken, so O=0. So, S+1+c=10, and S=8 or S=9.
Now, note that E+0+c = N or N+10 in E+0+c=N. E is at most 9, so E+0+c is
at most 10. To produce a carry, this would require N=0, but 0 is taken so
this column does NOT produce a carry. Moving to the left, this means S+1=10
or S=9. This leaves:
9END
+10RE
------
10NEY
From here, you can pursue the same sort of reasoning to discover R next,
then Y, E and N.
Have fun!
Mike.