Olympiad in Mathematics (6 class)

1. Write down all the natural numbers divisible by 2 lying on the numerical beam between 1992 and 2007.
2. Cut the rectangle into 3 triangles so that only 1 is rectangular.
3. How to use a 7-liter bucket and a 3-liter can to pour exactly 5 liters of water into a pan?
4. The older brother walks from home to school for 30 minutes, and the younger one for 40 minutes. After how many minutes will the older brother catch up with the younger one if he left 5 minutes earlier?
5. From 12345678910111213...5657585960, cross out 100 digits so that the remaining number is the largest.

Answers and decisions:

1. 1994, 1996, 1998, 2000, 2002, 2004, 2006.

2.

3. One solution:
using a 3-liter jar, pour 6 liters of water into a bucket. Once again pour 3 liters of water into the jar and fill the 7-liter bucket to the top. Then there will be 2 liters of water in the jar, which we will pour into the pan. Add to them 3 liters of water - we get only 5 liters of water.

4. The older brother will catch up with the younger in 15 minutes. If the younger brother came out 10 minutes earlier than the older brother, the older brother would catch up with the younger at school: 40-30 = 10 (min). So, in the case when the younger brother left 5 minutes earlier than the older brother, the older brother will catch up with the younger in the middle of the road. This distance the older brother will pass in 30:2 = 15 (min).

5. 99999785960 is the remaining number.

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