Continuous addend splitting
Example 1 How many ways are there to write 945 as the sum of continuous natural numbers?
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Analysis: Because 945=35×5×7, * * has (5+1)× (1+1)× (1+1) =16.
Therefore, 945*** can be divided into the sum of 16- 1= 15 (species) continuous natural numbers.
Can the sum of several continuous natural numbers be equal to 199 1? If so, how many different answers are there? Write these answers; If not, explain why.
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Analysis:1991=1×181,where * * has (1+1) × (/kloc)
So 199 1 can be divided into several consecutive natural numbers, and there are three answers.
from 199 1 = 1× 199 1:
199 1=995+996。
from 199 1 = 1 1× 18 1:
The second article
Digital separable feature
Example 142□28□ is a multiple of 99, and the quotient obtained by dividing this number by 99 is _ _.
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Analysis: Numbers divisible by 99 must be divisible by 9 and 1 1.
If the two digits A and B are filled with thousands and digits respectively, the sum of digits on each digit is [16+(a+b)]. To make the original number divisible by 9, [16+(a+b)] must be a multiple of 9, that is, the sum of (a+b) can only be 2 or 1 1.
In addition, the difference between the sum of odd digits and the sum of even digits is (8+a-b) or (b-a-8). To make the original number divisible by 1 1, it is necessary to make (8+a-b) or (b-a-8) 165438. It is verified that (b-a-8) is a multiple of 1 1.
So a-b=3.
If a+b=2 or 1 1, a=7 and b=4 can be obtained.
So it is easy to get the quotient of 427284÷99=43 16.
The third article
Discontinuous addend splitting
Example 1 Make a wire with a length of 144 cm into a rectangle with an integer length and width. * * * There are _ _ _ different ways to do it? What kind of rectangle is the area?
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Analysis: The sum of the length and width of a rectangle is
144÷2=72 (cm).
Because 72 =1+71= 2+70 = 3+69 = ... = 35+37 = 36+36,
So, there are 36 different methods.
Comparing the product of the length and width of each rectangle above, we can find that when the length and width are both 36 cm, the area is.