Brain Teasers and Puzzles

Hi everyone, thougt i would post this intersting one: 7 Sales executives have 1 million dollars to divide amongst themselves. The most senior sales executive propses a particular split and then everyone votes (each person's vote is equal). If at least 50% of the people accept, then the money is divided the way that was suggested. Otherwise the sales executive who propsed it gets fired...and then we move on to the next senior sales exec and the whole process repeats. The executives are rational (want to keep their jobs first and also get as much money as possible), and they also would prefer fewer executives in the group if given a choice (all else equal). How sho…

Hi folks. I've not posted in a while but thought of this site when a topic cropped up elsewhere. Apologies if it has already cropped up here but I didn't find anything with a quick search. It is standard in Europe to quote fuel consumption for a liquid-hydrocarbon-powered vehicle in volume of fuel burnt per distance covered. A small car may achieve 5 litres per 100 kilometres, for example. But if we convert both volume and distance to the same unit, millimetres, we get 5,000,000 cubic millilitres over 100,000,000 millimetres. This gives us an area of 0.05 square millimetres. With me so far?

If *C* is a Cube and *S1* is the Sphere Inscribed and *S2* is the Sphere Superscribed then (1) What is the fraction of the volume of *C* is contained in *S1* (2) How many times the volume of *S2* is that of *S1*

Why does the hourglass not start rising right away?

Here are n circles of radius r arranged in a closed string. The centers of the adjacent circles are connected with straight lines. What is the difference between the orange and the blue areas?

What is the mathematical equation in 2D and 3D for your body? Is there a mathematician in our world who could find the mathematical equation in 2D and 3D for their own body? For your information, 2D refers to surface equations, and 3D refers to volume equations. This passage is just for laughter and to encourage participants to try finding the equation for their own body: It's amusing that no mathematician has thought of writing their own body equation, who knows perhaps this equation hides a great mathematical secret.😀 Some legends about the city of Atlantis mention that the foundation of their highly advanced civilization, far more advanced than…

Cut a Cube into six identical pieces each having nine edges !

There are two traffic related threads going on right now, and here is a traffic related question which would've been OT in both, so I post it here. The points A and B are connected by two roads, APB and AQB. The section AP takes 20 minutes regardless of traffic. The section PB takes time equal to T/10, where T is the number of cars on the road. For example, if there are 200 cars on it, it takes 200/10 = 20 minutes. Similarly, AQ takes T/10 minutes and QB takes 20 minutes regardless of traffic. The city planners came up with an ingenious way of connecting points P and Q with a road that does not take any time at all regardless of traffic: …

This little hospital has 16 rooms connected as shown in the picture. There is one patient in each room. The patients in the rooms 2 to 16 are bedridden, but the patient in room 1 is fine and ready to go home. This patient wants to meet every other patient once, and only once, and then to exit the hospital from the room 16, as shown. How can it be done?

I've received this "riddle" from a friend this morning: Doing my best to translate it to English here, while cutting off irrelevant details. Bob got an electronic clock in shape of an apple. It shows time with a precision of a hundredth of a second. As he was moving down on an escalator, Bob threw the clock up and noticed that at the top of its trajectory the clock showed 11:32:45:81. His teacher Mary was moving up on the escalator at the same time, and she noticed that the clock showed 11:32:45:74 at the top of its trajectory. Find the speed of the escalators, given that they move with the same speed, at the angle of 300 to horizon. Ignore the air frictio…

I guess I'll start; You all want me, knowing I will hurt you, I'm oh so flattered you think me a virtue. If you let me in, good and bad times I will bring, I've won more battles than any man or king. Sometimes I'm dark, sometimes I shine, some think me a curse while others think me divine. If you guess my name, then I'll raise a toast, you'll be with the one who invites me the most.

I've stumbled upon this puzzle and immediately thought of @Trurl because they post about prime numbers often. Of course, others are welcome to try it as well.

Five aging pirates decided to split their treasure and to retire. Each one will be satisfied if in his estimate his share is not smaller than one fifth of the total. Their estimates vary. How can they do it peacefully?

I assume everyone here is familiar with the Monty Hall problem. I'm not looking for the solution. I'm not looking for another proof for the solution. I'm not even looking for a full game solution which might incidentally show how the 50:50 solution couldn't be correct.. The challenge is to directly figure out why the 50:50 answer is wrong but more importantly why it seems so axiomatically correct. I've had the solution for some time, but wasn't sure how to present it. Since it's become a classic logic riddle, I realized this was probably the best forum. At least I hope so, Im still pretty new here. I'll give it some time and provide a new hint every now …

A tribe of nomadic aliens is located in a planetary system that can supply them with sufficient resources to get to the next resource rich system. The next such system is 8 ly away, and there is only empty space in between. They can carry enough resources, a "load", to go 5 ly. They can make storages of any size on the way. What is the minimum amount of loads they will need to get to the next system? Is there a limit to the distance between systems that they can cross?

You have a rope and a lighter. If you light a rope, it burns about 1 m in 1 hour. However, it does not burn at a uniform rate, e.g., not necessarily 0.5 m in 0.5 hour. Can you measure 0.5 hour? 15 minutes? 20 minutes?

How tall is the table? BTW, I could not make ChatGPT answer this question correctly, with or without algebra.

I've prepared a simple toy: It consists of a pencil and a string that goes through a hole in the pencil and makes a loop. The ends of the string are glued together. The loop is shorter than the long end of the pencil: so, it can't be moved over it. Then, I insert the pencil through the buttonhole like this: This is how it looks from the other side: I can separate them again and repeat without cutting, breaking, untying, etc. Can you figure it out? I can take more pictures, from different angles, if you need. There are no hidden cuts or anything like it. You can make it yourself.

Imagine that you got planks 1m long each, as many of them as you wish. The planks have a width and a thickness, but those are not important here. What is important, they have weight. The only thing you can do with the planks is to put them on top of each other, like this: Your goal is to make the tower with the largest possible "shadow", x. IOW, the largest horizontal distance between the leftmost and the rightmost edges of the planks. The question is: what is the largest x so that the tower and its parts don't fall?

When a train moves forward there is always a part of it that moves backward relative to the ground. What part is it?

This is a pair of bar magnets one of which has been demagnetized. How to find out which is it without any other tools or materials?