In one move, it is permitted to either double a number or to erase its last digit. Is it possible to get the number 14 from the number 458 in a few moves?
An entire set of dominoes, except for 0-0, was laid out as shown in the figure. Different letters correspond to different numbers, the same – the same. The sum of the points in each line is 24. Try to restore the numbers.
In a room, there are 85 red and blue balloons. It is known that: 1) at least one of the balloons is red; 2) from each arbitrarily chosen pair of balloons at least one blue. How many red balloons are there in the room?
Is the number \(10^{2002} + 8\) divisible by 9?
Is the sum of the numbers \(1 + 2 + 3 + \dots + 1999\) divisible by 1999?
Try to read the word in the first figure, using the key (see the second figure).
Six chess players participated in a tournament. Each two participants of the tournament played one game against each other. How many games were played? How many games did each participant play? How many points did the chess players collect all together?
Try to make a square from a set of rods:
6 rods of length 1 cm, 3 rods of length 2 cm each, 6 rods of length 3 cm and 5 rods of length 4 cm. You are not able to break the rods or place them on top of one another.
Write a number instead of the space (in letters, not numbers!) to get a true sentence:
THIS SENTENCE HAS ... LETTERS
(Note that the dash does not count as a letter, i.e. the word twenty-two is made up of 9 letters).
Once Alice was in one of two countries – A or Z. She knows that all of the residents of country A always tell the truth, and all the inhabitants of country Z always lie. Moreover, they often go to visit each other. Can Alice, after asking a single question to the first person that she meets, find out which country she is in?