## Who Lives in the White House?

Puzzle.There are five houses of different colors next to each other equally spaced on the same road. In each house lives a man of a different profession.

- The blue house is adjacent to the mathematician’s and con-man’s houses.
- The first house on the left is green.
- The nurse lives immediately to the right of the mathematician.
- The teacher lives halfway between the plumber’s house and the yellow house.
- The nurse’s house is immediately to the right of the red house.

Who lives in the white house?

*Correction Nov 11, 2017. Replaced “the same distance from” with “halfway between” to eliminate the possibility of the plumber living in the yellow house. Thank you to my readers for catching this mistake and to Smylers for suggesting a correction.*

## Leo B.:

The puzzle is obviously rigged in a way to make “con-man” the answer.

23 October 2017, 3:50 pm## Konstantin:

Donald Tramp

23 October 2017, 4:04 pm## lvps1000vm:

It’s obviously rigged to hint that the President of the U.S. is a con-man!

23 October 2017, 7:34 pm## Bradley C Kuszmaul:

It’s possible for it to be the nurse:

Colors: green, blue, red, white, yellow

People: con, teacher, math, nurse, plumber

Assuming that when we say that the teacher lives the same distance from the plumber and the yellow house, it’s possible that they are the same house.

If we disallow the plumber living in the yellow house, then the conman solution is unique.

23 October 2017, 10:33 pm## Adam Hesterberg:

There are four solutions, of which I bet you didn’t intend the last three and would like to eliminate the last one:

GWBRY

PCTMN

GRBWY

TMNCP

GYRBW

TPMNC

GBRWY

24 October 2017, 12:06 pmCTMNP

## James Pfeiffer:

It’s true that there is an alternate solution. But I liked the puzzle aspect where you couldn’t derive the entire configuration – just the property that (C,W) were in the same location.

If we add the rule “The red house is not between the blue and white houses”, we eliminate the undesired solution but keep the three other solutions intact.

24 October 2017, 1:23 pm## Robert Clark:

I’m exploring the possibility there may be a graph theory approach to solving such logic problems in general. This may have applications to AI.

Bob Clark

26 October 2017, 3:14 am## Jeff Howard:

A beautiful problem. I like the idea of Robert Clark’s above of employing a graph theoretic method to solve the problem.

This reminds me of a website i saw the other day, lambdadesign.io, they seem to be about finding the beauty in mathematics. It’s nice that they’re trying to open people’s eyes to the fact that mathematics involves a lot more that equations and numbers.

—Jeff

28 October 2017, 7:10 pm## Smylers:

Adam’s final 3 solutions all have the plumber in the yellow house.

The question hints that the plumber’s house and the yellow house are separate. A tweak to the phrasing of the relevant statement could perhaps clarify that. Maybe something like: “The teacher lives halfway between the plumber’s house and the yellow house.”

7 November 2017, 9:55 am## jackbrain:

Thank you for updating this content.

14 November 2017, 4:50 am## incorrect:

The president and his/her family.

30 January 2018, 7:30 pm## Tanya Khovanova's Math Blog » Blog Archive » Mathy Review of the 2019 MIT Mystery Hunt:

[…] Now we have logic puzzles or another type, where you need to draw a grid. These are puzzles of the type: Who lives in the White House? […]

24 March 2020, 7:23 pm## scitamehtaM:

Please can someone send me a full solution ? I’m only just starting with these type of problems in my varsity course and I would really like to see how one would phrase the argument because I always lose marks for my arguments because of the way I phrase them.

1 August 2020, 1:10 am