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There are two cogwheels on a table. The bigger one has 10 teeth and is fixed to the table. The smaller one has 5 teeth and revolves around the bigger one. If the smaller cogwheel makes one full rotation around the bigger cogwheel, how many rotations will it make with respect to the table?
The answer is three rotations in total. Two because of the ratio 10:5, one more because of the movement of the smaller cogwheel.
Get from START to END in this planet maze, created by Sean Jackson.
The solution is shown below.
Three professors fell asleep under a tree. At some point a prankster passed by and painted their faces with black dye. When the professors woke up, each of them saw the others’ faces and started laughing at them. After a while though, they stopped laughing, realizing that their own faces were painted as well. How did they deduce that?
Let us denote the professors with A, B and C. The thought process of A would go like this: “If my face is not painted, then B will see that C is laughing at him and will realize immediately that he is being pranked. However, B was laughing for a while and therefore my I must being pranked as well.”. Then A will stop laughing and the same will happen with the other two professors B and C.
Louis has a bar of chocolate 4×6 which is marked into 24 little squares. At each step, he breaks up one of its pieces along any of the marked horizontal/vertical lines. Show that no matter how he does that, it will always take the same number of steps until the chocolate is broken into single 1×1 pieces.
Every time he splits the chocolate, the number of pieces increases by 1. Therefore it will always take him 23 steps to split it into single pieces.
Get from START to END in this maze, created by Sean Jackson.
The solution is shown below.
You are given 3 boxes – one labeled “Apples”, one labeled “Bananas”, and one labeled “Apples and Bananas”. You are told that the labels on the boxes have been completely mismatched, i.e. none of the three labels is put on its correct box. How can you open just one box and pick a random fruit from it, so that after seeing the fruit, you can guess correctly the contents of every box out of the three?
Open the box labeled “Apples and Bananas”. If you pick a banana from it, then the box labeled “Bananas” will contain apples, and therefore the box labeled “Apples” will contain apples and bananas. Similarly, if you pick an apple from it, then the box labeled “Apples” will contain bananas, and therefore the box labeled “Bananas” will contain apples and bananas”.
Three people check into a hotel room and each of them gets charged $10 – a total of $30. Later the clerk realizes that the bill is just $25, so he sends the bellboy to return $5 to the guests. On his way to the room, the bellboy decides to cheat and pockets $2 of the money, and gives the three men just one dollar each. Now the three men have spent $9 each, for a total of $27. Additionally, the bellboy took $2 for himself, which adds up to $27 + $2 = $29. Since the guests originally handed over $30, the question is what happened to the remaining $1?
The calculation is made the wrong way. The three men originally gave $30, but later $5 of them were sent back, which makes it $30 – 5 = $25 left at the clerk. Each of the men spent $9, so they gave $27 in total, $2 of which ended up in the bellboy’s pocket. $27 – $2 = $25, so no “missing dollar” here.
3 x $9 – $2 = $30 – $5.
Find a move for White, which does not result in a mate.
The move is Rc6+. Then Black can play Rxh7.
Get from START to FINISH in this maze, created by Joe Wos.
The solution is shown below.
Which creature walks on four legs in the morning, two legs in the afternoon, and three legs in the evening?
Man – four limbs as a toddler, two feet as an adult, two feet and a walking stick as an elderly.
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