Pinocchio and Pierrot were racing. Pierrot ran the entire race at the same speed, and Pinocchio ran half the way two times faster than Pierrot, and the second half twice as slow as Pierrot. Who won the race?
Try to decipher this excerpt from the book “Alice Through the Looking Glass”:
“Zkhq L xvh d zrug,” Kxpswb Gxpswb vdlg, lq udwkhu d vfruqixo wrqh, “lw phdqv mxvw zkdw L fkrrvh lw wr phdq – qhlwkhu pruh qru ohvv”.
The text is encrypted using the Caesar Cipher technique where each letter is replaced with a different letter a fixed number of places down in the alphabet. Note that the capital letters have not been removed from the encryption.
Find out the principles by which the numbers are depicted in the tables (shown in the figures below) and insert the missing number into the first table, and remove the extra number from the second table.
Everyone believed that the Dragon was one-eyed, two-eared, three-legged, four-nosed and five-headed. In fact, only four of these definitions form a certain pattern, and one is redundant. Which characteristic is unnecessary?
Jemima always tells the truth, but when she was asked the same question twice, she gave different answers. What kind of question could this be?
In a purse, there are 2 coins which make a total of 15 pence. One of them is not a five pence coin. What kind of coins are these?
What is there a greater number of: cats, except for those cats that are not named Fluffy, or animals named Fluffy, except for those that are not cats?
The angle at the top of a crane is \(20^{\circ}\). How will the magnitude of this angle change when looking at the crane with binoculars which triple the size of everything?
Given an endless piece of chequered paper with a cell side equal to one. The distance between two cells is the length of the shortest path parallel to cell lines from one cell to the other (it is considered the path of the center of a rook). What is the smallest number of colors to paint the board (each cell is painted with one color), so that two cells, located at a distance of 6, are always painted with different colors?
What is the minimum number of squares that need to be marked on a chessboard, so that:
1) There are no horizontally, vertically, or diagonally adjacent marked squares.
2) Adding any single new marked square breaks rule 1.