[3rd grade].
Fill in the eight numbers 2 9 in the figure on the right, so that the sum of the three numbers on each side is equal to 18.
Analysis] The number on the four corners is the number of overlaps, and the number of overlaps is 1 time. So the sum of the four overlapping numbers is equal to.
And among the eight known numbers, the sum of the four numbers is 28 only:
4 + 7 + 8 + 9 = 28 or 5 + 6 + 8 + 9 = 28.
And since 18-9-8 = 1, 1 is not one of the eight known numbers, so 8 and 9 can only be filled in diagonals. This gives us two ways to fill in the overlap number shown in the figure below left:
Fill in", only the filling method in the upper right picture matches the question.
The English word for the word "math" is "math". Use red, yellow, blue, green, and purple colors to dye the letters, and each letter is dyed in a different color. How many different ways can these colors be dyed?
Analysis] In order to complete the dyeing of the word "math", we can complete the dyeing process in four steps, in alphabetical order
Step 1 – Dye the letter "m", at this point there are 5 colors to choose from;
Step 2 – Dye the letter "a", since the letter "m" has already used one color, there are only 4 colors to choose from for the letter "a";
Step 3 – Dye the letter "t", since the letters "m" and "a" have already used up 2 colors, there are only 3 colors left to dye the letter "t";
Step 4 – Dye the letter "h", since the letters "m", "a" and "t" have already used up 3 colors, there are only 2 colors to choose from for dyeing the letter "h".
According to the principle of multiplication, a total of 5 4 3 2 = 120 different staining methods can be obtained
Grade 5] In the figure below, two cubes with sides of 10 and 15 are placed together to find the area of the triangle ABC (shaded part).
Analysis] The area of the triangle ADC is 10 15 2 = 75, and the height of the triangle ABC is 15 10 = 15 times, they are all based on BC, so the area of the triangle ABC is 1 of the triangle BCD5 times. The area of the shaded part is: 75÷（1＋1.5）×1.5=45。
Grade 6] As shown in the figure, ABCD is a square, which has been marked in the area chart of several shaded parts, find the area of the quadrilateral BMQN.
Analysis] Use the "half model" to solve this problem. For narrative convenience, the area in question is indicated in letters.
The area of cmd and and and the area are half of the area of the square ABCD, which constitutes half of the model. From this, we can see that and= abn+ cdn, the left and right sides of the equation are half the area of the square. From this we get the following equation:
a+100+c=30+a+b+18+c
b=100-30-18
The area of b=52b is the area of the quadrilateral bmqn.
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