A square piece of paper is cut into 6 pieces, each of which is a convex polygon. 5 of the pieces are lost, leaving only one piece in the form of a regular octagon (see the drawing). Is it possible to reconstruct the original square using just this information?
Try to get one billion \(1000000000\) by multiplying two whole numbers, in each of which there cannot be a single zero.
Ten people wanted to found a club. To do this, they need to collect a certain amount of entrance fees. If the organizers were five people more, then each of them would have to pay £100 less. How much money did each one pay?
At the cat show, 10 male cats and 19 female cats sit in a row where next to each female cat sits a fatter male cat. Prove that next to each male cat is a female cat, which is thinner than it.
The vendor has a cup weighing scales with unequal shoulders and weights. First he weighs the goods on one cup, then on the other, and takes the average weight. Does he deceive customers?
Teams A, B, C, D and E participated in a relay. Before the competition, five fans expressed the following forecasts.
1) team E will take 1st place, team C – 2nd;
2) team A will take 2nd place, D – 4th;
3) C – 3rd place, E – 5th;
4) C – 1st place, D – 4th;
5) A – 2nd place, C – 3rd.
In each forecast, one part was confirmed, and the other was not. What place did each team take?
In the race of six athletes, Andrew lagged behind Brian and two more athletes. Victor finished after Dennis, but before George. Dennis beat Brian, but still came after Eustace. What place did each athlete take?
We meet three people: Alex, Brian and Ben. One of them is an architect, the other is a baker and the third is an bus driver. One lives in Aberdeen, the other in Birmingham and the third in Brighton.
1) Ben is in Birmingham only for trips, and even then very rarely. However, all his relatives live in this city.
2) For two of these people the first letter of their name, the city they live in and their job is the same.
3) The wife of the architect is Ben’s younger sister.
Replace the letters in the word \(TRANSPORTIROVKA\) by numbers (different letters correspond to different numbers, but the same letters correspond to identical numbers) so that the inequality \(T > R > A > N < P <O < R < T > I > R > O < V < K < A\).
Restore the numbers. Restore the digits in the following example by dividing as is shown in the image