Olympiad in mathematics (6th grade)

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

Answers and solutions:

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

2.

3, One way to solve it is
with a 3-litre can, pour 6 liters of water into a bucket, pour 3 liters of water into the can again and fill the 7 liter bucket to the top Then there will be 2 liters of water left in the can, which we will pour into the pot. Add 3 liters of water to them - we get only 5 liters of water.

4, The older brother will catch up with the younger brother after 15 minutes If the younger brother had gone out 10 minutes before the older brother, then the older brother would have caught up with the younger brother at the school: 40-30=10 (min).So, in the case when the younger brother came out 5 minutes before the older brother, the older brother would have caught up with the younger brother in the middle of the way. This distance the older brother will pass in 30:2=15 (min).

5. 99999785960 - remaining number.

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