# How to solve a cryptarithm with multiple conditions

I'm trying to solve a cryptarithm that must meet all of the following conditions:

one + one = two

seven is prime

nine is a perfect square

More specifically, i'm trying to find the following:

one =

two =

seven =

nine =

Firstly, can someone explain the first condition (one + one = two) and how it fits in with the other conditons? Is this a sort of cryptarithm within a cryptarithm that must also stay true to the other conditions?

Secondly, what approach should I take to logically deduct the solution?

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Presumably, one is meant to assume that each of the letters o, n, e, t, w, s, v, i stands for a digit (maybe even a different digit) so one is a 3-digit number and so on. Now you make a lot of deductions along the lines of these:

The 1st condition tells you $o\le5$, and $o$ is even. The 2nd condition tells you $n$ is $1$, $3$, $7$, or $9$. The 3rd condition tells you $e$ is $1$, $4$, $5$, $6$, or $9$.

Collect enough of these bits of information and you have a chance of figuring out what each letter stands for.

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