Cheryl tells the month to Albert and the day to Bernard.
Albert: I don’t know the birthday, but I know Bernard doesn’t know either. Bernard: I didn’t know at first, but now I do know. Albert: Now I also know Cheryl’s birthday.
When is Cheryl’s birthday?
SOLUTION
If Albert knows that Bernard doesn’t know when the birthday is, then the birthday can’t be on May 19 or June 18. Also, Albert must know that the birthday can’t be on these dates, so May and June are completely ruled out.
If Bernard can deduce when the birthday is after Albert’s comment, then the birthday can’t be on 14th. The remaining possibilities are July 16, August 15, and August 17.
Finally, if Albert figures out when the birthday is after Bernard’s comment, then the date must be July 16.
All points on a circle are colored in blue and red colors. Show that you can inscribe inside the circle an isosceles triangle whose vertices have the same color.
SOLUTION
Inscribe a regular pentagon inside the circle. Three of its five vertices must have the same color, and they form an isosceles triangle.
Get a piece of paper with dimensions 9×12 with a 1×8 rectangular hole in the middle. Then, cut the paper into two pieces that can be arranged into a square. You can print out the shape below.
You wake up on a frozen lake in an isolated region, a hundred meters away from the shore. The surface of the lake is frictionless, and no grip of any kind can be attained over it. You find just your mobile phone in your pocket, but when you take it out to call for help, you realize there is no reception.
If there is no wind force to help you escape, what are you going to do to avoid freezing to death?
SOLUTION
Throw your phone as hard as you can. Thanks to Newton’s third law of motion and the frictionless lake, you will start sliding away.
In a small village, there are 100 married couples living. Everyone in the village lives by the following two rules:
If a husband cheats on his wife, and she figures it out, the husband gets killed on the very same day.
The wives gossip about all the infidelities in town, with the only exception that no woman is told whether her husband has cheated on her.
One day a traveler comes to the village and finds out that every man has cheated at least once on his wife. When he leaves, without being specific, he announces in front of everybody that at least one infidelity has occurred. What will happen in the next 100 days in the village?
SOLUTION
Let us first see what will happen if there are N married couples in the village and K husbands have cheated, where K=1 or 2.
If K = 1, then on the first day the cheating husband would get killed and nobody else will die. If K = 2, then on the first day nobody will get killed. During the second day, however, both women would think like this: “If my husband didn’t cheat on me, then the other woman would have immediately realized that she was being cheated on and would have killed her husband on the first day. This did not happen and therefore my husband has cheated on me.” Then both men will get killed on the second day.
Now assume that if there are N couples on the island and K husbands have cheated, then all K cheaters will get killed on day K. Let us examine what will happen if there are N + 1 couples on the island and L husbands have cheated.
Every woman would think like this: “If I assume that my husband didn’t cheat on me, then the behavior of the remaining N couples will not be influenced by my family’s presence on the island.” Therefore, she has to wait and see when and how many men will get killed in the village. After L days pass however and nobody gets killed, every woman who has been cheated on will realize that her assumption is wrong and will kill her husband on the next day. Therefore, if there are N + 1 couples on the island, again all L cheating husbands will get killed on day L.
Applying this inductive logic consecutively for 3 couples, 4 couples, 5 couples, etc., we see that when there are 100 married couples on the island, all men will get killed on day 100.
Warning: this puzzle involves mature themes that are inappropriate for younger audiences. If you are not an adult, please skip this puzzle.
SHOW PUZZLE
Mary is 21 years older than her son. After 6 years, she will be 5 times older than him. Where is the father?
SOLUTION
Let M be the age of the mother and S be the age of the son. We have M = S + 21 and M + 6 = 5(S + 6). We solve the system and get S= -3/4, i.e. minus 9 months. Therefore right now the son just got conceived and the father is with the mother.
