Naoki Inaba is a prolific Japanese puzzle author of over 400 original logic puzzles. His puzzles have been featured in both "The New York Times" and "The Guardian".
If you have 10 dots on the ground, can you always cover them with 10 pennies without the coins overlapping?
SOLUTION
Assume the dots lie in a plane and the radius of a penny is 1. Make an infinite grid of circles with radii 1, as shown on the picture, and place it randomly in the plane.
If we choose any point in the plane, the probability that it will end up inside some circle of the grid is equal to S(C)/S(H), where S(C) is the area of a coin and S(H) is the area of a regular hexagon circumscribed around it. A simple calculation shows that this ratio is larger than 90%. Therefore, the probability that some chosen point in the plane will not end up inside any circle is less than 10%. If we have 10 points, the probability that neither of them will end up inside a circle is less than 100%. Therefore, we can place the grid in the plane in such a way that every dot ends up in some circle. Now, just place the given coins where these circles are.
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.
I caused my mother’s death and didn’t get convicted. I married 100 women and never got divorced. I got born before my father, but I am considered perfectly normal?
Who am I?
SOLUTION
A priest, whose mother dies from labor, who marries 100 women to 100 men, and whose father attends his birth.
After you die, you somehow appear in a mystical room with two doors and two keepers inside. One of the doors leads to Heaven and the other door leads to Hell. One of the keepers is always lying and the other keeper is always saying the truth. If you can ask one of the keepers whatever question you want (you don’t know which keeper is lying and which one is truthful), how can you find your way to Heaven?
SOLUTION
You can point your finger to one of the two rooms and ask any of the keepers the question “If I ask the other keeper whether this room leads to Heaven, would he say YES?”. If the answer is NO, go through that door, if the answer is YES, go through the other one.
Look carefully at the picture below and answer the questions.
1. How many tourists are staying at this camp? 2. When did they arrive: today or a few days ago? 3. How did they get here? 4. How far away is the closest village? 5. Where does the wind blow: from the north or from the south? 6. What time of day is it? 7. Where did Alex go? 8. Who was on duty yesterday? (Give their name) 9. What day is it today?
SOLUTION
1. There are 4 people. 2. They arrived a few days ago, enough so that a spider web can appear on the tent. 3. Judging by the paddles, they got there with boats. 4. There is a hen walking around the camp, so the closest village is not far away. 5. The leaves of the trees are larger at the south side, so the wind must be blowing from the South. 6. The shadow is pointing towards West, so it must be morning. 7. Alex went to catch butterflies. 8. Since Peter is on duty today – cooking food for the group, it was Colin on duty yesterday. 9. Today is August 8. Watermelons ripen in August.
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