6 replies to this topic

[bonanova]

An odd number of guests at a party play a game.

When the music stops, the guests stand still while their host measures and confirms the distance between each pair of guests is unique. They are then instructed to keep an eye on the nearest other guest.

Every guest is thus watching some one.
But is every guest being watched?

[vistaptb]

Spoiler for

There will never be a case in which everyone is watched. If you take the shortest distance between two people, those people will always be watching each other. If you take the shortest distance that doesn't include those people, the people involved in that distance will also be guaranteed to watch each other. You can continue pairing people off like this until there is only the odd man out, who is being watched by nobody.

[edwindurock]

No, Nobody is watching the host.

[bonanova]

Spoiler for

There will never be a case in which everyone is watched. If you take the shortest distance between two people, those people will always be watching each other. If you take the shortest distance that doesn't include those people, the people involved in that distance will also be guaranteed to watch each other. You can continue pairing people off like this until there is only the odd man out, who is being watched by nobody.

Close, but ..

Spoiler for maybe not

You have not shown the the next shortest distance that does not include the first pair involves people who will be watching each other.

[bonanova]

No, Nobody is watching the host.

Good point.
But that was not what the puzzle meant to ask.

OP Has been appropriately edited.

[vistaptb]

Spoiler for

There will never be a case in which everyone is watched. If you take the shortest distance between two people, those people will always be watching each other. If you take the shortest distance that doesn't include those people, the people involved in that distance will also be guaranteed to watch each other. You can continue pairing people off like this until there is only the odd man out, who is being watched by nobody.

Close, but ..

Spoiler for maybe not

You have not shown the the next shortest distance that does not include the first pair involves people who will be watching each other.

Spoiler for

Well, if one of those people is watching someone in the original pair instead of the other person, then someone will have to be unwatched because two people are watching the same person (the one in the original pair).

[bonanova]

Now you have it. Good solve.