[Tasks]

QUANTUM
for younger students

1. The bottle, glass, jug and jar contain milk, lemonade, kvass and water. It is known that water and milk are not in a bottle, a vessel with lemonade stands between a jug and a vessel with kvass, there is neither lemonade nor water in a jar. The glass stands next to the jar and vessel with milk. Where is each liquid poured?
2. figure shows a target. Where do you need to go and how many shots do you need to make to get 100 points?
3. Find the x and y digits of a five-digit number 42x4y if you know that this number is divisible by 72.
4. Which numbers are more numerous among the first million: those in whose notation there is a unit, or those in whose notation there is one?
5. Given a square of size 5x5, in which 25 numbers are written (see figure). Let’s choose one of the numbers (arbitrarily), circle it, and cross out the remaining numbers in the same column and in the same line. Then we select one of the remaining numbers, circle it, and cross out the remaining numbers in the same line and column. Let’s do this five times.
   Let’s take the sum of the circled numbers. It turns out that no matter how we choose the numbers, this sum is always equal to 56. Try to unravel this hinn-steven property of the reduced square.

A. P. Savin
V. M. Rosentuller

42x4y
72

16
17
23
24
39
40

4 0 8 12 2
7 3 11 15 5
10 6 14 18 3
13 9 17 21 14
16 12 20 24 14