Clue glossary
Number Puzzle Clues Explained: Digits, Ranges and Remainders
The clues use ordinary properties of a candidate number: its size, parity, individual digits, digit sum or remainder after division. Knowing exactly what each statement tests makes elimination quicker and more reliable.
Parity and comparisons
A number is even when it divides by 2 exactly; otherwise it is odd. A clue saying 'greater than 50' excludes 50, while 'between 50 and 80' includes the stated endpoints in these puzzles. Apply the wording to the complete number before examining its digits.
- 68 is even and greater than 50.
- 50 is not greater than 50.
- A range check is a quick first pass through the register.
Digit position and digit sum
The first digit is the leftmost digit and the last digit is the rightmost. For 472, the first digit is 4, the last is 2, and the digit sum is 4 + 7 + 2 = 13. A clue about containing a digit only asks whether it appears anywhere. A clue about the count of even digits asks how many individual digits are even; zero counts as even.
- 472 contains 7 but does not end in 7.
- The digit sum of 472 is 13, not 472.
- In 402, all three digits are even.
Remainders
If a clue says a number leaves remainder 2 when divided by 5, divide the candidate by 5 and inspect what is left over. For 47, 5 × 9 = 45, leaving 2, so 47 passes. For 45, nothing is left over, so it fails. A digit-sum remainder clue first adds the digits, then divides that sum.
- 47 divided by 5 leaves 2.
- The digit sum of 47 is 11; 11 divided by 3 leaves 2.
- Do not confuse a remainder of 0 with an even number.