Problem 30 · 2020 Math Kangaroo
Stretch
Logic & Word Problems
Number Theory
caseworkwork-backward
The clues below help identify a four-digit number N:
- 2741 — one digit is right, but it is in the wrong place.
- 4132 — two digits are right, but they are in the wrong places.
- 7642 — none of the digits are right.
- 9826 — one digit is right and in the right place.
- 5079 — two digits are right; one is in the right place and the other is in the wrong place.
What is the hundreds digit of the number N?
Show answer
Answer: A — 0
Show hints
Hint 1 of 2
The clue '7642: none right' deletes the digits 7, 6, 4, 2 from N entirely — that prunes the others fast.
Still stuck? Show hint 2 →
Hint 2 of 2
Use the place/value hints to pin each digit; then read off the hundreds digit.
Show solution
Approach: eliminate, then place the surviving digits
- Clue 7642 (none right) removes 7, 6, 4 and 2 from N, simplifying the other clues.
- Working through the remaining position clues forces N = 9013 (the only number fitting all five hints).
- Its hundreds digit is 0.
- The answer is 0, choice A.
Mark:
· log in to save