Russian version of the site: тюе.рф
YOUNG NATURALISTS TOURNAMENT
is a competition among teams of school students (12 – 16 years old) in their ability to solve
complicated problems in natural science and defend these solutions in public discussion.
The Tournament will be presented in September on the site http://www.ynt2012.org
and in Russian journal “Potential”
Participants of the Tournament – teams of 6 school students from Russia and other countries.
Problems of the Tournament are challenges of natural science and math
and will be published at http://www.ynt2012.org
Supposed dates for the Tournament:
Preliminary competitions (electronic – and video-conference) –
from 15 September to 15 November 2012.
Russian final competition – December 2012.
International final competition – April 2013.
The registration of participants of the Tournament
will be open from 21 September 2012.
Young Naturalists’ Tournament
Problems for the correspondence rounds
1. The fishermen and the fish.
After having caught enough fish, three fishermen went to sleep and decided to divide their catch the next morning. The first fisherman woke up earlier than the others and decided to take his part of catch not waiting for the others to wake. He has split the catch into three parts equal by fish number, but one fish was left extra. So het let the extra fish out to the river, took his part and left. Then the second fisherman woke up. He didn’t spot that the first fisherman was gone and decided to take his part of catch, not waiting for the others to wake. The same thing happened to him as to the first fisherman: he split the catch, let out the extra fish, took his part and left. The same happened to the third fisherman.
1. How many fish there were in the catch?
2. How many fish there were in the catch, if there were four fisherman?
3. Let there were initially N fisherman, and each of them made the same what the fishermen made in the first case? How many fish there were in the catch?
2. Candle experiment.
Put a burning candle into a plate filled with water. Now cover the candle with a transparent beaker. Explain the observed physical phenomena. Investigate the dependence of the magnitude of water level rise in the beaker on different relavant parameters.
3. Atomic mass.
Introduce a method to determine the atomic mass of an unknown chemical element in the conditions of a school chemical lab.
4. Orange lichen.
On the trunk of a separately standing tree you have found an orange lichen (Xanthoria parietina). On the north side of the trunk the lichen is green, on the western and the eastern sides it is yellow, on the southern side it is orange. How can the difference in lichen colors be explained? Propose a method to test your hypothesis.
5. Sparrow nights.
In the month of June, nights are short in Russia, with the shortest night on June 22. Then, until December 22, the length of night increases. This increase is due to both the later sunrise and the earlier sunset. How and why does this happen?
6. Center of mass of a triangle.
The median of a triangle divides it into two equivalent triangles (i.e. of the equal areas).
The three medians of a triangle divide it into six equivalent triangles; in other words, if x,y,z,u,v,w stay for the areas of the small triangles (fig.1), then x = y = z = u = v = w.
The main goal of the creative task is in determining the links between the area equalities of a certain number of small triangles (i.e. the equality of some set of the numbers x,y,z,u,v,w) and the existence of, at least, one median among the segments AD, BE, CF on fig.1.
1. Prove, that the point G inside the triangle ABC belongs to the median AD if and only if [ABG] = [CAG], where [Ф] here and everywhere stays for the area of the figure Ф. Use the fig.2, where the additional constructions were made.
2. Prove that the point G inside the triangle ABC is the median intersection point (fig.2) if and only if [АВG] = [ВСG] = [САG].
3. For the given triangle ABC find all the points G of the plane, for which [АВG] = [ВСG] = [САG].
4. Prove that if six (or some five) numbers from x,y,z,u,v,w are equal, then all three segments AD, BE, CF on fig.1 are medians.
5. Prove that if some four numbers from x,y,z,u,v,w are equal, then all three segments AD, BE, CF on fig.1 are medians.
6. Is it true that if some three numbers from x,y,z,u,v,w are equal, then all three segments AD, BE, CF on fig.1 are medians.
7. What can be said about the existence among the segments AD, BE, CF (fig.1) of at least one median, if it is known than only two of the numbers x,y,z,u,v,w are equal?
7. Electrical resistance.
Two metal shovels are plugged into ground at some distance from each other. Measure the electrical resistance between them. Find the dependence of this resistance on the distance between the shovels. If possible, investigate the dependence of this resistance on the other parameters.
8. Illusionist chemist.
The illusionist chemist puts six identical beakers on the table. The beakers are half-filled with a colorless fluid. Then he takes a flask also filled with a colorless fluid, and puts some of this fluid to the first beaker. The fluid in the beaker turns dark blue. An attendee is invited to add the fluid from the flask to the five other beakers – all stay colorless! Then the illusionist orders each of the beakers to turn a particular color, and it happens right under is command! What is the secret of the trick? Repeat this trick.
A recently synthesized substance was delivered to a microbiological lab to test its antibiotic activity. There are the components of the growing media (agar-agar, sugar, mineral salts), an autoclave, a desiccator and lab glassware in the lab. It is necessary to test the bactericide and fungicide activities of the substance. Propose an experimental routine. Can you make such an investigation in home conditions?
10. «Silver» water.
It is argued that the water held in a silver vessel for a long time possess some special properties. What properties and why?
11. Invent yourself.
Formulate a tournament problem on your own, and solve it.