Urgently, some math Olympiad questions!! 5

As can be seen from the title, this sequence does not contain 6,7,8,9, that is, all the numbers in the sequence are composed of 0,1,2,3,4,5, so this sequence is essentially a sequence of numbers in the hexadecimal system.

Considering that you are not familiar with the hexadecimal system, here is a brief description.

For example, if you consider this sequence in hexadecimal system, the first number is 0, the second number is 1, the 6th number is 5, and the 7th number cannot be written as "6", it should be written as "10", and this hexadecimal 10, it is actually the 6 in the decimal system, which is our natural number 6. (1 in 10 represents 1x6, 1 represents 0x6 0, and the two digits of 1 and 0 together are 6).

According to the title, 0 is also a non-negative number, so if the 2010 items referred to in the question are calculated from 1, they should be 2009 items, (it is easier to understand the number from 1).

Convert the decimal number 2009 to 6 to get 13145

The method of converting decimal to 6 decimal is as follows:

Divide 2009 by 6 to take the remainder, divide the resulting quotient by 6, and then take the remainder until the quotient is 0, take the remainder.

Combine the remainders in reverse order, i.e., hexadecimal"2009"In addition, all conversions from decimal to other decimal systems are made in this way, and when converted to decimal system, divide by the number.

The base hexadecimal system is relatively rare, the common ones are binary, base 8, and base 16, and the base hexadecimal here is only.

It is used for the convenience of this question.

You can enter up to 999 words here, don't be lazy, it's actually to arrange the hexadecimal numbers from small to large.

Convert 2010 to hexadecimal. (2010)10=(13150)6The 2010th number is 13150

The whole can be or be recommended

$4. The smallest unit of angular angle, so the money spent must be a multiple of 23.

People are an integer, so the number of people participating in the interest group must be an integer multiple of 17 and 23, and less than 780, so it is 391. Therefore, 389 people did not participate.

In the same way, the number of boys in each class must be a multiple of 7 and 4, and less than 150 3, so it is 28, and the answer is 21.

1 He ended up with 4 yuan left.

2. There were 379 students who did not participate in the mathematics interest group.

3. The number of girls in the third class is 21.