Riddles
These are some of my favorite riddles. Solutions are not given!
I know what you know
Two people are trying to find two numbers. The first person knows only the sum of the two numbers, the second person knows only the product.
They have this conversation:
- (Person that knows sum): “I am certain that you do not know the numbers.”
- (Person that knows product): “That’s right, and I still do not know the numbers.”
- (Person that knows sum): “But I do know the numbers.”
- (Person that knows product): “And so do I.”
What are the numbers? (They are not 0 or 1).
Forging a chain
A woman enters a jeweller shop. She explains to the jeweller that she has four chains of three links each, and she wants to have it forged to a whole circle of 12 links. The jeweller says it costs 10 euros per link that he has to break and mend. The woman agrees with this and leaves the shop.
The next day she returns and is very happy to see the chain exactly as she wanted it. The jeweller is pleased with this and asks her to pay her 40 euros. The woman looks at him and says she doesn’t agree to this.
Is the jeweller overcharging her?
The two envelopes
I have two envelopes: one contains twice as much money as the other. I let you choose one envelope and give it to you. You open it up and are happy to find 10 euros in it. But, I give you a chance to reconsider and trade the envelope you have for the envelope I have. So you risk to lose 5 euros but could gain 10. This sounds like a good idea! Or isn’t it?
The prisoner with the quiet mind
(This one I still find a little hard to grasp myself…)
A prisoner is to be hanged withing the next 30 days, but is granted a last wish. This is a very cunning prisoner, and he doesn’t like smoking, so he requests the following: to not know when he wakes up in the morning, that this day will for certain be the day of his execution. His executioner laughs and agrees, a simple wish to fulfill, it seems.
But all is not so simple. Would you agree he couldn’t be executioned on the last of the 30 days? Then the prisoner would be certain it would be the day of his execution. What about the 29th day? Would an execution on the 16th come as a surprise? Which days are good then?
Make 24
Using the numbers 3, 3, 8, and 8, and the four basic operations +,-,/,* make 24.
Mixing oil and vinegar
You have a bottle with oil and a bottle with vinegar. Both are equal amounts. I take one spoonful from the vinegar and throw it with the oil. I stir well, and take a spoonful of the mixture and add it to the vinegar. Neither are good dressings for salad now, but the question is, which of the mixtures is more pure? What if I don’t stir well?
Galilei invariance
For this puzzle you need to know high-school physics. It works effectively on subjects that took a course on special relativity. Physicists often understand complicated matter, but are displeased to realize there are many simple things they don’t understand.
A car travels at speed v1. It accelerates, and reaches a speed v2. Assuming a perfect engine, how much energy was used to increase the velocity? We take two viewpoints: an observer A standing still on the road, and an observer B who rides his bike at velocity v1. Galilei invariance tells us that the laws of nature apply to both viewpoints, in particular they would agree on how much energy (i.e. gasoline) was used to accelerate the car.
Now, observer A claims that the car in first instant had a kinetic energy of (1/2)m(v1)^2, and after acceleration had a kinetic energy of (1/2)m(v2)^2. The energy difference is therefore (1/2)m((v2)^2-(v1)^2). Observer B says that the car started at speed zero, but accelerated to a speed of v2-v1. So the difference in kinetic energy is (1/2)m(v2-v1)^2. Both start argueing viciously about who’s right. Can you explain the difference?
To hang a painting
A painting has a rope that goes around in a loop. You can hang the painting on one nail. If you pull the nail out, the painting will fall. Can you hang the painting on two nails, so that if you pull ANY nail, the painting falls down? How about three nails?
Guess the color of your hat
Three people are given a hat that is either blue or red. You cannot see your own hat, but you can see all other hats. Nobody is allowed to talk or give signals. Everybody should guess the color of his/her own hat, or say nothing, but this should be done at the same time. If somebody guesses his/her color correctly, and nobody guesses incorrectly, you all win. Before you get the hats you can decide together on the best strategy. Can you get a success rate of more then 50%? This can also be done with 4,5, etc. people.
Twelve golden balls
You are given twelve golden balls. They have all the same weight, except one is different, but you don’t know if it’s heavier or lighter than the others. You must determine which one it is, and whether it is heavier or lighter, using a balance and only three weighings.
The left-over square
Consider a field of squares 1024 on each side. The total number of squares is then 1024×1024. Of course, you cannot fill the field with copies of this figure:
* **
because the total number of squares is not divisible by three. Consider that one square should be left over in the end, can you fill the rest of the field with copies? Where can this left-over square be?