Harry and Matt came down from a mountain. Harry walked on foot, and Matt went skiing, which was seven times faster than Harry. Halfway down, Matt fell, broke his skis and his leg, and hence travelled twice as slow as Harry. Who will descend first from the mountain?
Is it possible to transport 50 stone blocks, whose masses are equal to \(370, 372,\dots, 468\) kg, from a quarry on seven 3-tonne trucks?
On every cell of a \(9 \times 9\) board there is a beetle. At the sound of a whistle, every beetle crawls onto one of the diagonally neighbouring cells. Note that, in some cells, there may be more than one beetle, and some cells will be unoccupied.
Prove that there will be at least 9 unoccupied cells.
Is it possible to fill an \(n\times n\) table with the numbers \(-1\), \(0\), \(1\), such that the sums of all the rows, columns, and diagonals are unique?
One and a half diggers dig for a half hour and end up having dug half a pit. How many pits will two diggers dig in two hours?
Sam and Lena have several chocolates, each weighing not more than 100 grams. No matter how they share these chocolates, one of them will have a total weight of chocolate that does not exceed 100 grams. What is the maximum total weight of all of the chocolates?
Two friends went simultaneously from A to B. The first went by bicycle, the second – by car at a speed five times faster than the first. Halfway along the route, the car was in an accident, and the rest of the way the motorist walked on foot at a speed half of the speed of the cyclist. Which of them arrived at B first?
Andrew drives his car at a speed of 60 km/h. He wants to travel every kilometre 1 minute faster. By how much should he increase his speed?
A tourist walked 3.5 hours, and for every period of time, in one hour, he walked exactly 5 km. Does this mean that his average speed is 5 km/h?
In a volleyball tournament teams play each other once. A win gives the team 1 point, a loss 0 points. It is known that at one point in the tournament all of the teams had different numbers of points. How many points did the team in second last place have at the end of the tournament, and what was the result of its match against the eventually winning team?