Even number in 20.2.1.12.5.9.31.120.30.23.45.11?

Even number in 20.2.1.12.5.9.31.120.30.23.45.11?

20,2,12,120,30

Put a pile of apples into some boxes. If each box contains 8 apples, there are 12 apples left. If each box contains 9 apples, there are still 3 apples left to fill the last box. The total number of apples is 3______ An apple, yes______ It's a box

(12 + 3) △ 9-8, = 15 △ 1, = 15 (pieces), 15 × 8 + 12, = 120 + 12, = 132 (pieces); answer: there are 132 apples and 15 boxes

If you put seven apples in six boxes, there will always be at least two apples in one box. Why?
In a basketball game, a player shoots 8 times and gets 17 points. The player has at least one three-point shot. Why
There are 367 students in Guangming primary school. Are there two students whose birthdays are on the same day? Why
There are five red, yellow, blue and green balls in your pocket. How many can you find at least at one time to ensure that there are two balls of the same color?

Basketball 2 * 8 = 16 is one point less, so at least one of them is three points
367 students have at least two birthdays, because the year is 366 days at most (leap year), everyone is different, there is one more person
Four color ball at least five at a time to ensure that there are two same ball, because touch four may not be the same

A total of 43 apples, respectively, in 6 boxes, each box put odd, how to put
I thought about it all night, but I didn't think about it

Odd number odd number addition equals odd number, even number odd number addition equals even number, even number box containing odd number is equal to even number odd number addition, must be equal to even number. But the total number in the question is odd number, we can't use the conventional method. Because we don't explain the size of the box, we can assume that the sixth box can pack the first five, and the question becomes odd number box (5) containing each odd number, There are many solutions

There are five red, yellow and blue balls in a box. At least how many balls should be taken out to ensure that two balls are of the same color? At least how many balls should be taken out to have three balls of the same color
And why, determinant!

At least 3 + 1 = 4 balls must be taken out to ensure that two balls are of the same color
At least 3x2 + 1 = 7, there are 3 of the same color

There are 12 red, yellow, blue and white balls of the same size in the box. If you want to find two pairs of balls of the same color, you need to touch at least () balls? Please explain the process and reasons in detail

4 + 3 = 7
In the worst case, first touch one different color, so four, then touch three, there will be three of the same color, three have two of the same color, three have three different colors, but there will always be two pairs of the same color!

There are eight small balls in four colors of red, yellow, blue and white, which are mixed in one cassette. At least a few balls need to be touched in order to ensure that there are three small balls in the same color?

There are eight small balls in four colors of red, yellow, blue and white, which are mixed in one cassette. At least 17 balls need to be touched in order to ensure that there are three small balls in the same color?
The worst case is to touch 8 color balls and then touch 8 color balls
Touch one more
8+8+1 = 17