Will the quotient or the remainder change if a divided number and the divisor are increased by 3 times?
Try to get one billion \(1000000000\) by multiplying two whole numbers, in each of which there cannot be a single zero.
Decipher the puzzle:
Decipher the puzzle: \(KIS + KSI = ISK\). The same letters correspond to the same numbers, different letters correspond to different numbers.
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?
Two tribes live on the island: natives and newcomers. It is known that the natives always tell the truth and the newcomers always lie. A traveler hired an indigenous islander as a guide. On the way, they met a man. The traveler asked the guide to find out which tribe this person belongs to. The guide returned and said that the man said that he was a native. Who was the guide – a native or a newcomer?
Among 40 containers there are two containers of different shapes and two containers of different colors. Prove that among them there are two containers that are both of different shapes and colors.
A cube with a side of 1 m was sawn into cubes with a side of 1 cm and they were in a row (along a straight line). How long was the line?
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?