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Living Maths

Take your mind for a walk and try these teasers just for fun

New questions will be posed each Monday and the answers posted the following Friday. Test your friends and colleagues.

See below for the answers to the following teasers.

Teaser #1.

If it takes five men six hours to dig seven holes, how long does it take one man to dig half a hole?

Teaser #2.

The windows on all four sides of my house face South. How is this possible?

Teaser #3.

Three people in a room are standing in a line (single file), facing in one
direction. They cannot communicate with each other and there are no
reflective devices (Mirrors, windows, etc.) in the room. A bag with 5
hats (three white and two black) is placed in the room. Each person in the
room is given a hat each (Randomly assigned). No one gets to see their own hat or what is left in the bag. The person at the back of the line can see the hats of the two people in front of him/her. The second person can only see the hat of the person in front of him/her. The person in the front can see no-one's hat. The three people are told that if they know what colour their hat is, they must then leave the room. After about 10 minutes, the person in the front of the line leaves the room first. What was the colour of his/her hat and how did s/he work this out?

Answers

Thank you to all those who sent in their answers. While most people got number 2 and 3 correct, number 1 produced some interesting results. See below how you faired:

Teaser 1:

You cannot get half a hole!

However, from readers' emails, the following answer was common: 2.14 hours. It takes 6 hours per five men for seven holes, that is 6/7 hours for five men for one hole, or (6x5)/7 hours per one man per hole, or (6x5)/(7x2)=2.14 hours per one man per half a hole.

Teaser 2:

The house was built in the North Pole

Teaser 3:

The colour of the hat was white.

We start off by saying WHAT IF

If the last person can see two black hats in front of them then THEY would
have left the room (they would have certainly had a white hat). Since they
did not leave, this means that they did not see two black hats in front of
them.

This suggests that we either have a black and white, white and black or
white and white scenario for the two front people.

If the first person is wearing black then the middle person would think that
they are either wearing white or black - if the person in front of them was
wearing black and they themselves were wearing a black hat then the last
person would have left BUT they did not. This would mean that the
middle person would then think that they have a white hat and then they would have left too. BUT they did not. Therefore, the middle person could not have seen a black hat in front of them. The front person works
through all these situations in their own mind and realizes that through
deduction, they must have a white hat. They then leave the room.