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Number Play

Letters for digits

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.

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This track

  1. 0 Start here
  2. 1 What a digit sum remembers
  3. 2 Why adding the digits knows anything
  4. 3 Odd and even, multiplied
  5. 4 Turn it round and subtract
  6. 5 Several clues at once
  7. 6 The case that breaks it
  8. 7 Saying why, in order
  9. 8 Odd and even, added
  10. 9 Magic squares
  11. 10 Counting rhythms
  12. 11 Letters for digits
  13. 12 Even or odd expressions
  14. 13 Checkpoint: sums, squares and sequences
  15. 14 The big picture
  16. 15 Track quiz

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