Students will solve logic puzzles where letters replace digits in arithmetic operations.
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One letter = One digit.
Introduce cryptarithms.
Have you ever tried doing arithmetic where the numbers are hiding behind letters?
In these math puzzles, called cryptarithms or alphametics, each letter stands for a specific digit from 0 to 9. Your job is to act as a math detective and crack the code!
Vertical addition layouts must be clearly formatted to mimic standard algorithmic addition.
In a cryptarithm, the vertical layout helps you align units and tens to track the carrying logic.
Explain place value logic for cryptarithms.
When faced with a cryptarithm, don't just guess numbers randomly. Always start by looking at the units place to establish constraints and limit your possibilities.
Worked example of T+T+T=UT.
Problem. Solve the cryptarithm where a single digit is added three times to produce a two-digit sum:
Faded example for K2+K2=HMM.
Let's solve the cryptarithm .
Step 1: First, look at the units place. We add the given digits: . Since the sum ends in , the letter must represent the digit .
Step 2: Now look at the tens place. The addition is . Because we found that is , the two-digit sum must actually end in . Therefore, must equal .
Step 3: Since , we divide by 2 to find that is . This leaves the hundreds place , which must be the carry-over digit .
Check understanding of carry-over limits.
In the cryptarithm , what is the only possible value for in the hundreds place?