The first article: social investigation
A math team went to Anwar community to do a social survey. The math group asked the street director, "How many people are there in your community?" The street director said humorously, "The last four digits of 5 1995 are the population of my community!" It turns out that the director is a retired math teacher. The students in the group quickly worked out the population of Anwar community. Students, do the math.
Answer and analysis:
Starting from 55, the product is four digits.
The last four digits of 55=3 125 56 are 5625 57, 8 125 58, 0625 59 and 3 125. ...
Observing the above calculation result 2, it is quickly found that the last four digits of 5n change regularly from 55, and appear once every three digits: 3 125, 5625, 8 125, 0625, 3 125, 5625, 8/kloc-.
1995 ÷ 4 = 498 ...3 So, the last four digits of 5 1995 are 8 125, and the population of Anhua community is 8 125.
Article 2: 100 bunting
Arrange a street from east to west according to the rules of five red flags, three yellow flags, four green flags and two flags, and hang 1995 colorful flags. Can you guess the color of the100th colorful flag from west to east?
Answer and analysis:
From west to east, the100th colorful flag is a positive number from east to west.
This is the key to answering this question correctly.
The 100 bunting from west to east is equivalent to the 1896 bunting from east to west, because1995-100+1=1896 is called "five red, three yellow, four green two powders".
1896 ÷ (5+3+4+2) =135 ... 6 The remainder is 6, so the colored flag on the positive number1896 is yellow.
Chapter III: Money in the passbook
Someone went to the bank to withdraw money. For the first time, he took more than half of his deposit in 50 yuan, and the remaining half was 100 yuan for the second time. At this time, there is 1350 yuan left on his passbook card. Q: How much money does he have on his passbook card?
Answer and analysis: it can be reversed, and the remaining half is 100 yuan for the second time. We know that "the remaining half exceeds 100 yuan" is 1350, so the remaining half is1350-100 =1250.
The remaining money is: 1250×2=2500 yuan.
Similarly, when I visited the remaining half of 50 yuan for the first time, I could see that the "remaining half is less than 50 yuan" was 2500, so the "remaining half" was 2500+50=2550 (yuan).
The original passbook card is 2550×2=5 100 yuan.
This problem is mainly based on the idea of reduction. The general feature of the reduction problem is that it is known that four operations are performed on a certain number in a certain order, and we usually perform the corresponding inverse operations in the opposite order of operation or increase or decrease.
Chapter Four: Factorizing prime factors to find the age.
There are four children, one of whom is just older than the other 1 year. The product of their ages is 360, so how old is one of them?
Answer and analysis: factorization prime factor method
Judging from the above solving process, it is complicated to solve problems by algebraic method, and sometimes, when solving mathematical problems, the arithmetic method is relatively simple. This is often used when dealing with some problems in middle schools. Especially when answering multiple-choice and fill-in-the-blank questions.
360=23×32×5;
Then, according to the meaning of the question, the six arrays decomposed above are synthesized into the product of four numbers, namely:
360=3×4×5×6; The obvious age is 6 years old.
Chapter 5: Three factors.
/kloc-What is the number with only three factors between 0/00 and 300?
Answer and analysis: Through the answer to the above question, we know that "the number of factors of a complete square number is odd", and a number with only three factors between 100 and 300 must be a complete square number. But is it clear that all factors of a complete square number are three? Let's study that 42= 16 is a complete square number, and its number of factors is 42=24. According to the learned theorem of number of factors, the number of factors of 16 is 4+ 1=5. Did the students find any patterns? There are only three factors in the square of prime numbers, such as 22, 32, 52, 72, 1 12, 132, ... We turn the problem into finding "which numbers are the square of prime numbers between 100 and 300".
Answer: Because the square of a prime number has only three factors, there are only seven complete squares between 100 and 300:12, 122, ... 172, but only1/kloc-. So there are only three factors:112 =1,132= 169, 172=289.