Not a Unique Solution

Logic Level 3

The following cryptarithm has three solutions -

$\overline{\mathsf{ON}} \times 3 = \overline{\mathsf{GO}}$ .

Find the sum of all the three values of $\mathsf{O}$ .

This problem is a part of my set Numbers in Disguise - Cryptarithms .

The answer is 6.

2 solutions

Ameya Salankar
May 1, 2014

The three solutions to the cryptarithm are:

$17 \times 3 = 51$ , $24 \times 3 = 72$ & $31 \times 3 = 93$ .

The sum of all the possible values of $\mathsf{O}$ is:

$1 + 2 + 3 = \boxed{6}$ .

the same solution as me!!!

Thư Hồ - 7 years ago

You can cheat at this one based on what your problem asks to answer , since a 2 digit number multiplied by 3 give a 2 digit number O should be less than 4 since 4 is the smallest value that multiplied by 3 will give a 3 digit number , a better question would have been maybe asking how many solutions does the problem have but nice problem anyways.

A A - 5 years, 2 months ago

Mj M
May 16, 2014

Numbers 4, 5, 6, 7, 8, and 9, when used as tens digit, will give answers more than 2 places, leaving us with 1, 2 and 3 as possible tens digits. Hence, 1+2+3=6.

Not a Unique Solution

The answer is 6.

2 solutions

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