Letters= numbers

[dave7]

cook + cooks + a = snack k, s and a are single digits. When you sum them, how do you work out whether to bring 0 , 1 or 2 units to the next line ? Same goes for the next columns. Thanks.

 

[soroban]

Hello, dave7!

Your instructions are strange . . .

. . \(\displaystyle \begin{array}{ccccc}^1 & ^2 & ^3 & ^4 & ^5 \\
&C&O&O&K \\ C&O&O&K&S \\ + &&&&A \\ \hline S&N&A&C&K\end{array}\)


K, S and A are single digits.
What about C, O and N ?

When you sum them, how do you work out whether to bring 0 , 1 or 2 units to the next line?
Why 0, 1 or 2? .Why not 5 or 8?

In column-5, we see that: \(\displaystyle K + S + A\) ends in \(\displaystyle K.\)
. . Hence, \(\displaystyle S + A \,=\,10\) and there is "one to carry" to column-2.
Let \(\displaystyle c_5\) mean "the carry from column-5."

In column-4, we see that: \(\displaystyle O + K + c_5\) ends in \(\displaystyle C.\)
. . There is a carry of \(\displaystyle c_4\), which could be zero.

In column-3, we see that: \(\displaystyle O + O + c_4\) ends in \(\displaystyle A.\)
. . There is a carry of \(\displaystyle c_3\) which could be zero.

In column-2, we see that: \(\displaystyle C + O + c_3\) ends in \(\displaystyle N.\)
. . And there is definitely a carry: \(\displaystyle c_2 = 1.\)

In column-1, we see that: \(\displaystyle C + 1 \;=\;S\)


I suspect that there is sufficient information for a unique solution.
A considerable amount of Guessing is involved.