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Can you cover the chess board with 31 domino pieces, such that only two opposite corners are left uncovered?
The answer is NO. Every domino piece covers exactly one black and one white square on the chess board. Since initially you start with a different number of available white and black squares on the chess board, it is impossible to cover it with domino pieces.
Can you arrange 6 new identical pencils in space such that every two of them touch each other? What if you have 7 pencils?
Remark: The construction doesn’t need to be stable.
Below you can see solutions for 6 and 7 pencils. The construction with 6 pencils is stable, the construction with 7 pencils – not.
Move only 2 matchsticks, so that the fly will escape from the trap. The shape of the trap must remain the same.
The solution is shown below.
You have unlimited number of knights, bishops, rooks and kings. What is the biggest number of pieces (any combination) you can place on a chessboard, so that no piece is attacked by another one?
If we put 32 knights on all black squares, then no two pieces will attack each other. Now let’s see that if we have more than 32 pieces, then there will be two which attack each other. Split the chessboard in 8 rectangular sectors of size 2×4. It is not hard to see that if we have more than 4 pieces in the same 2×4 sector, then 2 of them will attack each other. Therefore we can place at most 4 × 8 = 32 pieces on the chessboard.
In certain society all parents stop having children right after they get their first boy. After 1000 years, approximately what will be the percentage of the women in the society?
The answer is 50%. The reason is that no matter what birth plan the society comes up with, the chance for having a boy or a girl during every birth is 50/50.
In what countries a man can not marry his widow’s sister?
In no country, a man can marry his widow’s sister, because he would be dead.
Get from START to FINISH in this “Atomic Energy” maze, created by David Modray.
The solution is shown below.
A man stands in the center of a circular field which is encompassed by a narrow ring of water. In the water there is a shark which is swimming four times as fast as the man is running. Can the man escape the field and get past the water to safety?
Yes, he can. Let the radius of the field is R and its center I. First the man should start running along a circle with center I and radius slightly less than R/4. His angular speed will be larger than the angular speed of the shark, so he can keep running until gets opposite to it with respect to I. Then, the man should dash away (in a straight line) towards the water. Since he will need to cover approximately 3R/4 distance and the shark will have to cover approximately 3.14R distance, the man will have enough time to escape.
What follows next in the following sequence:
1, 11, 21, 1112, 3112, 211213, 312213, ?
Every term in the sequence describes how many 1s, 2s, 3s, etc. were there in the previous term. “11” means that in the previous term there was one 1. “21” means that in the previous term there were two 1s. “1112” means that in the previous term there were one 1 and one 2. “3112” means that in the previous term there were three 1s and one 2. “211213” means that in the previous term there were two 1s, one 2 and one 3. “312213” means that in the previous term there were three 1s, two 2s and one 3. Therefore, the next number in the sequence should be 212223.
You encounter three Gods in a room – the God of Truth, the God of Lie and the God of Uncertainty. You don’t know which one is which, but know that the God of Truth always says the truth, the God of Lie always says the lie and the God of Uncertainty sometimes lies and sometimes says the truth. You can ask in succession each of the Gods a unique question, to which they can reply only with “Yes” or “No”. However, their responses will be in their native language – “Da” or “Ne”, and you don’t know which translation to which answer corresponds. Your task is to figure out what questions to ask the Gods, so that will recognize which one of them is the God of Truth, which one is the God of Lie and which one is the God of Uncertainty.
Label the gods with numbers – 1, 2, and 3.
First, ask god 1 “If I ask you whether god 2 is random, would you say ‘Da’?”. If he responds “Da”, then god 3 is not the god of uncertainty. If he responds “Ne”, then god 2 is not the god of uncertainty. In both cases we will be able to find a god which is not the god of uncertainty, let without of generality that is god 3.
Next, ask god 3 “If I ask you whether you are the God of Lie, would you say ‘Da’?”. If he says “Da”, then he is the God of Truth. If he says “No”, then he is the God of Lie.
Finally, ask god 3 whether god 1 is the God of Uncertainty and conclude the identities of all gods.
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