Encrypted arithmetic puzzle of addition: EAT and THAT are added to produce the result APPLE. Each letter is a different number. Find the letters values.
The encrypted arithmetic puzzle of addition
Each letter represents a different number. Find the value of each letter.
Recommended time to solve 5 minutes.
You must be knowing addition rules!
Solution to the Cryptarithmetic puzzle
Analyze most significant letter of result
- Mathematical logic: The most significant letter A of the five digit encrypted number APPLE is a result of adding overflow from stage 3 (addition of E and H) and letter T. Both E and H being of maximum value 9, overflow to stage 4 must be 1.
- T also being of maximum value 9, overflow to stage 5 to produce result A must be 1.
- A = 1.
Analyze stage 4 results P
- To create a overflow of 1 to stage 5 with the help of an overflow of 1 from previous stage 3 (addition of E and H), T must have the maximum possible value of 9.
- Automatically, P takes the value of 0.
Analyze the result of first stage addition as value of T is now known
- As T = 9, addition of two 9s results in 18, overflow 1 and unit digit 8.
- E = 8.
Analyze third stage of addition
With E = 8 to produce a sum of 10 (1 overflow and P = 0), H must be 2.
Analyze second stage of addition
- L = 1 + 1 + 1 (overflow) = 3.
Solution to the Cryptarithmetic puzzle
A = 1, E = 8, H = 2, L = 3, P = 0 and T = 9.
Quite simple, isn't it?
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