Examples of Olympic Mathematics in Primary School 1:
There are red, yellow, blue and green beads in the same bag, and each color of beads is enough. How many beads must be taken at a time to ensure that two of them must be the same color?
Answer and analysis:
Take 1 bead for each kind, and four of them have different colors. If you take another one, there must be two beads of the same color, so you need five.
Primary school olympiad problem example 2:
(1) has a four-digit number, and its product multiplied by 9 is exactly the new four-digit number obtained by reversing the order of the original four-digit number. Find the original four digits.
(2) There is a four-digit number, multiplied by four. The product is just a new four-digit number, which is obtained by reversing the order of the original four-digit number. Find the original four digits.
Answer and analysis:
Or use abcd to represent the original four digits:
(1)abcd*9=dcba, four digits multiplied by 9 do not carry, obviously a= 1, d = 9；;
Looking at hundreds, hundreds have no carry, and it is easy to get b=0 and c=8.
So the original four digits are 1089.
(2)abcd*4=dcba, look at thousands first, because there is no carry, A is even, so A can only be 2; So, d = 8；;
Elementary school olympiad example 3:
The sum of nine different positive integers is 220. What is the maximum sum of the smallest five positive integers?
Answer and analysis:
In order to make the smallest five positive integers as big as possible, we should make these nine different numbers as close as possible. Because 220=20+2 1++28+4, the closest situation of these 9 numbers is 220 = 20+21+22+23+24+26+27+28+29.
20+21+22+23+24 = 1 10, so the maximum value of the sum of the smallest five positive integers is110.