Aaron, Bruce, Colin, and Dean are four men standing in a straight line, not necessarily in that order. The following is known about them:
- Precisely one man is fair, handsome, and unscarred.
- Two men who are not fair, are each standing next to Aaron.
- Bruce is the only man standing next to exactly one handsome man.
- Colin is the only man not standing next to exactly one scarred man.
Determine who is fair, handsome, and unscarred.
From #2, Aaron is one of the two in the middle. WLOG we can place him in position 2.
A, B and D are each standing next to exactly one scarred man. Since that includes Aaron, of positions 1 and 3, one of them is scarred and one is not.
SUUU UUSU
SSUU USSU
SSUS USSS
SUUS UUSS
Remembering that three, including A in position 2, must be standing next to exactly one S.
In SUUU, only A is standing next to exactly one scarred man so that's out.
In SSUU, positions 1, 2 and 3 are next to exactly one scarred man. That's a possibility
In SSUS, only positions 1 and 2 are next to exactly one scarred man so that's out.
In SUUS, only positions 2 and 3 are next to exactly one scarred man so that's out.
In UUSU, only positions 2 and 4 are next to exactly one scarred man so that's out.
In USSU, all four positions are next to exactly one scarred man so that's out.
In USSS, only positions 1 and 4 are next to exactly one scarred man so that's out.
In UUSS, only positions 2 and 4 are next to exactly one scarred man so that's out.
So SSUU is the only possibility, and Aaron is in position 2 and Colin in position 4. Only the man in position 3, either Bruce or Dean, or Colin himself, in position 4, could be the man we're looking for.
But the men standing next to Arron, and therefore in positions 1 and 3, are not Fair. That leaves perfection to Colin.
As a check, can he be handsome? Yes, I guess he can, so long as Bruce is in position 3 and Aaron is not handsome, and Dean in position 1 is not handsome either.
DABC
uuuH ugly vs Handsome
uFuF unfair vs Fair
ssUU scarred vs Unscarred
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Posted by Charlie
on 2022-01-20 18:01:25 |
solution
