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Lesson 11 of 16

Letters for digits

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7 min

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A + BA + BA = AA. Each letter stands for one digit. BA is a two-digit number, not B × A. Which digits?

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Set the puzzle out in columns.
Step 1 of 4
  1. Set the puzzle out in columns.
  2. Units: A + A + A ends in A. Take one A away: 2 × A ends in 0.
  3. A is 5, not 0, because AA cannot start with 0. The units sum is 15. Carry 1.
  4. Tens: B + B + 1 = 5. So B = 2.

The rule

A is 5 and B is 2.

The units column holds the last digit of each number.

In these puzzles each letter is one digit. Different letters are different digits. A number does not start with 0. Start at the units column.

Check the answer: 5 + 25 + 25 = 55. That is AA, with A = 5.

Work one column at a time. The units column gives a digit and a carry. Here 5 + 5 + 5 = 15, so write 5 and carry 1. The carry is added in the next column: 2 + 2 + 1 = 5.

Try the lab to finish this lesson.