Question

if AB×AB=ACB solve the cryptarithm

Answer 1

Given:

AB×AB=ACB

To Solve:

The cryptarithm.

Solution:

• AB represent a 2 digit number with A at 10s place and B at units place.

We are multiplying AB with AB.

• A and B can take any values from 0 to 9.

But If We multiply B by B to get B itself at the units place of the product,

• B can be 0 , 1 , 5, 6 .

• Also A should be at the 10s place ,  therefore  middle term should not have any carry over.
• Middle term is AB + AB = C

• Therefore B cannot be 5 or 6 .
• Also A cannot be 5 or 6.
• Therefore A and B can be 0 or 1

If we assume B and C to be different numbers , B cannot be 0 , as this makes C also 0.

• Therefore, B = 1
• Then A also 1
• C = AB + BA = 2

Therefore AB = 11, AB×AB=ACB  and ACB = 121