In short: Logic puzzles are solved by using the clues one at a time. Draw a diagram, list the possible cases and test each one, work backwards when you know the end, and check your answer against every clue.
Before you start
- Odd and even numbers, multiples and remainders.
- Adding columns with carrying.
- Working backwards (see Solving Equations).
Ordering puzzles
Digit clue puzzles
Letter sums (cryptarithms)
Each letter stands for a different digit.
Remainder puzzles
Working backwards
"I'm thinking of a number. I multiply it by 15 and add 36 to get 141." Undo in reverse: , then .
"Kristy spent 36 dollars and 43 dollars and had 32 dollars left." She started with dollars.
- Draw a line
- Place one clue at a time
- List the cases
- Cross out what fails
- Look at the last column
- Check for carrying
- One less is a common multiple
- Undo in reverse order
Quick summary
- Draw a diagram for ordering puzzles and add one clue at a time.
- When few cases are possible, list them all and test each one.
- In letter sums, start with the units column and think about carrying.
- If a number leaves remainder 1 for several divisors, one less than it is a common multiple.
- Work backwards by undoing each step in reverse.
- Always check your answer against every clue.
Quiz
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Try 3 questions now
I multiply a number by 6 and subtract 7 to get 59. What is the number?
- A 9
- B 11
- C 10
- D 12
Show answer
B: 11
Undo: , then .
Kristy spent 36 dollars on a skateboard and 43 dollars on a jacket. She had 32 dollars left. How much did she start with?
- A 79 dollars
- B 111 dollars
- C 101 dollars
- D 75 dollars
Show answer
B: 111 dollars
.
I multiply a number by 15 and add 36 to get 141. What is the number?
- A 7
- B 9
- C 11
- D 105
Show answer
A: 7
and .