In Dotland, people have dots on their foreheads. The dots come in two colors, red and blue. If anyone figures out what color dot they have on their forehead, they commit suicide.

The residents of Dotland have a tradition. Everyday they gather at the town-hall.

Everyone in Dotland is really smart. So if it is possible for them to figure out what color they have, *they will figure it out*.

It is given that at least one of them has a red dot and at least one of them has a blue dot.

Prove that they will all commit suicide.

Click here to see all the problems posted so far. Keep checking everyday!

## Comments

Sort by:

TopNewestThat is such a sad ending. They should be celebrating because they are so smart to figure out the color of their dot. – Calvin Lin Staff · 2 years, 11 months ago

Log in to reply

– Joshua Ong · 2 years, 11 months ago

Pessimists rule!Log in to reply

From the question it is evident that the people were excited to do suicide and if given chance could do suicide as quickly as possible. Let us assume that there exists a point of time in the day when they can do suicide. Suppose a number of people stay at the island, say 100. Suppose there is only one person with a blue spot rest 99 have red colours. Then on the festival the person with the blue spot could easily figure out the colour of his spot as he would see 99 red spots and as there should be at least 1 spot defferent from others so he will on the same day commit suicide and the rest people would think that as he on the same day committed suicide this means that there were only one blue colour and there colour was red , so they will also commit suicide. NoW suppose there are 2 blue persons so each of them will see one blue colour and 98 red . They ( each of the two blue persons ) Will think that if there colour would be red then the other blue person should commit suicide on the same day and if I too am blue then he too would be in doubt that if he is blue or red as I am, so he will wait till next day as he is not certain what would be his colour and would come next day to see if the other blue person has done suicide or nor , and he would think if he has I am red if he has not I am blue. So they both will be dead on the second day. Others being equally smart would use the same logic and would see two blue colors. They will think that if they are red then there would be two suicides on second day but if they are blue there would be three blue persons so the other two blue persons would be still alive on the third day and will come to see if the other two blue person are dead or not, if they are that means there were only two blue persons if not then there are three including myself. In this way they can figure what colour their own head is. To make this even more clear let us take an example of the case when there are three blue colours , then each one of them will come till the third day , on the second day from the gather, to find out that the other two blue persons are dead or not , If they are that means there were only two blue persons and they have figured out their colour as the way prescribed and if not he too himself is of same colour. In this way they can figure out the colour of the spots in their heads. If given a certain number such that the number of people of each colour is not equal and the number of people of the colour in minority is n then the minority would dead in the nth day if we count the first meeting of the people as the first day. And the other in majority would be dead in the next day . If the number of people of each colour is equal then they all would be dead in the nth day.Hence, proved – Utkarsh Dwivedi · 2 years, 11 months ago

Log in to reply

This is similar to & derived from the famous blue-eyes puzzle. Here's the solution of that . – Sagnik Saha · 2 years, 11 months ago

Log in to reply