Almost August!

Logic Level 2

Each letter in the following cryptogram represents a distinct, single-digit, positive integer.

Which of the following cannot be a value of $A?$

$\begin{array}{cccccc} \large & & \color{#D61F06}J & \color{#3D99F6}U & \color{#20A900}L & \color{#69047E}Y\\ \large & & & \color{#3D99F6}U & \color{#20A900}L & \color{#69047E}Y\\ \large & & & & \color{#20A900}L & \color{#69047E}Y\\ \large +& & & & & \color{#69047E}Y\\ \hline \large & & A & A & A & A \end{array}$

The given cryptarithm is similar to this one featured in the weekly problems, but the setup is different.

2 4 6 8

1 solution

Noel Lo
Jul 23, 2018

If $A=8$ , then based on the rightmost column, $Y=2$ . There is no carry over to the tens column so for $3L$ to give a number ending in $8$ , the only posssibility is $L=6$ so that $3L=18$ , but this would result in a carry over of 1 to the hundreds column and we have $2U+1$ as a number ending in 8. Considering that $2U+1$ is always odd while any number ending in 8 is always even, this is impossible!!

Almost August!

1 solution

0 pending reports