MYSTERY CODEmedium
Crack the 3-digit code.
All three digits are different.
WHAT'S THE CODE?
Clues
- 047One digit is correct and in the right place.
- 198One digit is correct but in the wrong place.
- 150Two digits are correct, both in the wrong places.
- 623No digit is correct.
- 783One digit is correct but in the wrong place.
Answer
517
Why it works
The clues eliminate every alternative and place 5, 1, and 7 in that order.
- From 623, the digits 6, 2, and 3 are not in the code.
- In 783, the 3 is already excluded, so exactly one of 7 or 8 is in the code, and it is in the wrong place.
- Suppose 8 were in the code. Then 198 would exclude 1 and 9, so 150 would force 5 and 0 into the code. The 047 clue would put 0 first, leaving 5 third and 8 second—but 8 is second in 783, contradicting the requirement that it be in the wrong place. Therefore 8 is absent and 7 is present.
- In 047, 7 must be the one correct digit in the right place, so the third digit is 7 and neither 0 nor 4 is used.
- With 0 excluded, 150 says 1 and 5 are both present but misplaced. The 1 cannot be first and the 5 cannot be second, so the only order is 5, 1, 7.