**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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