Letter Substitution
Math Concepts:
Add / Subtract- multi-digit numbers
Materials: Paper, pencil
Players: 1+
Challenge: Find the values of the letters in these puzzles. The three rules for letters are:
- A given letter is always the same digit (0 to 9)
- The left most digit of a number is never 0
- Different letters must be different digits
Create:
Make these puzzles by taking an addition or subtraction problem and replacing one or more of the
digits, as in the following examples:
Create puzzles to make interesting problem-solving challenges for your students. Note that the values of the letters do not carry over from puzzle to puzzle.
Discussion and Tips
One very useful observation is that when you add two numbers in a column, even if there is a carry of 1 into that column, the largest possible carry out of that column is 1 (9 + 9 + 1 = 19). For example, in the problem above where BA + BB=CAB, thev alue of C must be 1. Also, anytime you spot something like A + B = B, as in that problem, that will force A = 0 (as long as there is no carry into that column, which there isn’t).
Any problem involving the addition of two numbers can be rewritten as a subtraction problem instead. For example, BA + BB = CAB is the same as CAB- BA = BB.