Mixed III

1991/12/01 Angulo, Patxi Iturria: Elhuyar aldizkaria

• Matematika

Christmas holidays allow us to enjoy this little break we deserve. However, our habit of working does not leave our heads calm and many times we are doing some work for home. To avoid that, we offer 25 questionnaires to entertain you in these prestigious days.

1. Below are three houses and deposits of water, light and gas located in plane (a). Neighborhoods want to connect their homes with guards, but without crossing the pipes. Would it help them?

At the bottom (b), the houses and guards are located on donut floor. Neighborhoods have the same problem. Will they get the solution?

2. You have to form an eight-poxpole image with four triangles and two squares.

3. You have to make four straight cuts to a square. With the pieces obtained you will have to complete five equal squares.

4º Cut the side image in two equal parts.

5. If you draw a square in the emptied balloon, what will it look like after inflating the balloon?

6. How would you take out the paper without touching the woods?

7. A man comes home at night. He soon realizes something and commits suicide by taking the gun. But if he had seen sawdust on the floor of his house he would not have been killed. What is the cause of this strange behavior?

8th. Suppose someone has multiplied all the first numbers (of course those that are known). If the product is L:

• What is the latest L figure?
• the last figure is odd or even?

9. Three brothers lie three days a week, and in other cases tell the truth. The boss lies on Mondays, Tuesdays and Wednesdays. Those in the center on Wednesday, Thursday and Friday. The youngest on Fridays, Saturdays and Sundays. Once in Loyola, the three brothers gathered together, they said:

Nerea: today Friday is Josune: yesterday Thursday was Gorka: Josune is the main

What day of the week did this interview take place? What are the older people, the media and the younger?

10. Just as leaving the number of poxpoles on both sides of the symbol, how to make equality?

11. On one side of a card you can read the phrase “on this card there are two affirmations”. On the other side, the phrase “what is said behind is not true.” What is the lie?

12. In two forests we have water and wine, the same amount. Five drops are taken from the water and added to the wine. After shaking this forest, five drops are taken that are left in the water forest. Is there more water in the wine that came? Or the other way around?

13. In total, seven sultans have 2,879 women. There is no equal amount. If we divide the number of women in any of the rows by the number of others, we will always get the integer.

So say Allah, how many women there are in each party.

14. I went up to a cherry tree.

I did not eat cherries, but left it without cherries.

How many cherries were in the tree?

15. With the following pieces the chess table must be completed. The pieces can be rotated in the plane, but not in space.

16. A chess problem is to place the king, the lady, two towers, two bishops (in different colors) and two horses without attacking each other on a table of the 5x6 grids.

You can enter a difficulty. A pawn will be placed in the same conditions, but not in the first and last row.

17. Here is a division in which only 5 and 0 are seen. You must replace the dots with numbers to know the division.

18. Place the numbers 1 to 12 in white circles so that the sums of the six numbers of the rings are equal.

19. Now similar, but this time with numbers from 1 to 19, so that the sum in the lines of three circles (including radios) is 22. Once this is achieved, replace the numbers so that the sum is 23.

20. There are three cards face down. We know that to the right of a 1 there are 2 or 2; to the left of a 2 there are 2 or 2; to the left of a cup there is one or two swords and, finally, to the right of a sword there is one or two swords. What are the three cards?

21. With four sections suitable for the adjacent square you can get a four-vertex star.

22. In the image you can see a rectangle formed by L-shaped tiles. This rectangle has a slot that divides into two rectangles. The smallest rectangle that can be made without L-shaped tile slots is half the figure. But what is next?

23. Another division. In it odd numbers are represented by squares and pairs by circles. It is an exact division.

24. The centers of the circumferences of the figure are located in points P and Q, being the length of the PQ segment of 3 cm. What is the length of the MN segment passing through a cut-off point and parallel to the PQ?

25. Here are two pyramids. At both ends the lengths are equal. What are the volumes of the pyramids? (no calculation).

If you have a gap between games to try to answer these questions, thank you very much. Surely you have achieved it and you will not have to ask for answers. However, if you haven't tried it (you're still on time) or if, despite trying it, you haven't found all the answers, you'd like to have it checked or to know the ones you haven't found. In such a case, please let us know and tell you that you will receive the appropriate answer.