7
$\begingroup$

On a certain road there are 32 houses in a row, numbered 1 through 32, each inhabited by a single person. During the month of January each house is hosting a dinner date. House 1 on January 1, house 2 on January 2, and so forth. The occupant of house 32 is a lovable misanthrope, so he never has anyone over.

Every house follows the same dinner date etiquette:

  • The guest may arrive bearing one bottle of wine, but it is not mandatory.
  • When the guest arrives, if there is no wine in the house then tea is served.
  • If there is one bottle of wine in the house, it is wisely saved for later and, again, tea is served.
  • If there are two bottles of wine in the house, they drink one bottle of wine with dinner and in a state of intoxicated generosity give the other bottle to the person next door (the next higher numbered house).
  • In the rare case that a house finds itself in possession of three or more bottles of wine one is served with dinner, one is given to the person at the next higher numbered house and the rest is saved for later.
  • No one drinks wine except during a date, and every bottle opened is finished. No partials. No one dates anyone from the neighborhood. In short, no lateral thinking funny business.

On the morning of January 1, each house contains one bottle of wine except houses 3, 5, 11, 12, 17, 18, 24, 28 and of course 32. These nine houses contained no wine at all.

On the morning of February 1, each house contained one bottle of wine except 1, 5, 7, 8, 11, 12, 16, 20, 22, 25, 27, 28, and 29. These thirteen houses contained no wine at all. The gentleman in house 32 graciously accepted a bottle but has not drunk it, as per etiquette.

Which houses received a dinner date bearing a bottle of wine?

$\endgroup$
4
$\begingroup$

There is a simple mathematical pattern here:

Straightforward binary addition.

The answer can therefore be determined from:

11100010110101110111001100101110 - 1110111011111001111001111101011 = 01101011010110100111111101000011

and therefore bottles of wine were brought to houses:

1, 2, 7, 9, 10, 11, 12, 13, 14, 15, 18, 20, 21, 23, 25, 26, 28, 30, 31

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.