There are four troll brothers – Wudhor, Xhaqan, Yijlob, and Zrowag.
You must ask these brothers four YES/NO questions (one troll per question), and figure out their names. What questions would you ask?
Coming soon.
Prove that you can not cover the plane with infinite strips which have
Take a circle with radius 1 in the plane. A strip with width X covers at most an area of 2X of the circle. Therefore all strips cover at most an area of 2, which is smaller than the total area of the circle (~3.14).
52 cards – 2 of clubs to Ace of clubs, 2 of diamonds to Ace of diamonds, 2 of hearts to Ace of hearts, and 2 of spades to Ace of spades – are arranged in a deck. We shuffle them in the following manner:
Show that this method shuffles the deck uniformly, i.e. every permutation has the same chance to appear.
Notice that at all times the cards below the King of spades are shuffled uniformly. Therefore at the end, after we put the King of spades in a random place inside the deck, the entire shuffle will be uniform as well.
Can you construct a convex polyhedron, such that no two of its faces have the same number of edges?
No, you can not construct such a polyhedron. Assume the opposite and consider its face, which has the largest number of sides, say k. Then the polyhedron contains at least k more faces with different numbers of sides, all less than m. However, this is clearly impossible.
Someone stole gold coins from a museum near the park. No one saw the thief take the coins, so there isn’t a description of the robber. Slylock Fox suspects one of the creatures in the park is the thief. Which one?
The raccoon on the seesaw couldn’t hold the heavier bear off the ground unless he was carrying something heavy. Since gold is one of the heaviest metals, Slylock suspects the raccoon is the thief and has hidden the coins in his clothes.
Six pawns are placed in the middle squares of the main diagonal of a chess board – b7, c6, d5, e4, f3, g2. You are allowed to take any pawn on the chessboard and replace it with two pawns – one on the square above it and one on the square on its right, in case there are empty squares there. If after several moves there are no more pawns on the main diagonal, show that all the squares above it except for h8 are covered by pawns.
Assign the following weights on the squares of the chessboard:
Every time you make the splitting move, the total sum of the numbers of the squares covered by pawns remains a constant. At the beginning that sum is 6. Since 7/2 + 6/4 + 5/8 + 4/16+ 3/32 + 2/64 = 6, all 27 squares above the main diagonal, except the top-right corner (on which you can not place a pawn in any way), must be covered by pawns at the end.
If you know that the following game has been monochromatic, i.e. no piece has moved from black to white square or vice-versa, which one is the correct position of the bishop – e3 or e4?
The correct position of the bishop is e3. Otherwise, no White’s piece could have captured the last Black’s piece, moving on black squares.
There are several pieces of coal, a carrot, and a scarf lying on a lawn. If nobody placed them there, how did they end up like that?
Somebody made a snowman which melted within a few days.
You are given an 8×8 chess-board, and in each of its cells
Consider the intervals spanned by the numbers in the first row, second row, third row, etc. If all of these intervals intersect each other, then there is a number, which appears in all of them. If not, there are two intervals, which are disjoint, and a number between them, which does not appear in the two rows. Now it is easy to see that this particular number will appear in every column.
While changing a tire, a motorist accidentally dropped all four wheel nuts into the sewer grate. Just when the man lost all hope to retrieve the nuts and continue on his way, a kid passed by. After hearing the story, the kid gave an advice, which enabled the driver to successfully fit a new
The kid suggested that the man uses one bolt from each of the other three wheels to fix the fourth one.
Please confirm you want to block this member.
You will no longer be able to:
Please allow a few minutes for this process to complete.
