The probability that the sum of 3 numbers can be divided by 3

The probability that the sum of 3 numbers can be divided by 3

The above-mentioned two people's ideas of solving problems are too traditional and too pedagogical; the noumenon should open up new ways to better understand, which is also an idea of solving this kind of problems: (as follows): "the probability that the sum of the three numbers can be divided by three if you take any three numbers from 1 to 30" ∵ "there are 4060 ways to take any three numbers from 1 to 30" ∵ - as

1. The probability of the number that can be divided by 3; 2. The probability of the number that can be divided by 3 but not by 4; 3;
Supplement: 3. The probability of the number divided by 3 or 4;

Supplement
3. The probability of the number divided by 3 or 4
The probability of the number of numbers divisible by 3 is 100 △ 3 = 33 (take integer)
33 percent
The probability of the number divisible by 4 is 100 △ 4 = 25
It's 25 percent

The probability that any integer from 1 to 100 can be divided by 2 or 3 at the same time

（50+33-16）/100 =0.67

For a four digit number, its ten and one digit numbers are all 5. This number minus six can be divided by seven, minus seven can be divided by eight, minus eight can be divided by nine

7055

There is a four digit number, the number on the thousand and the number on the hundred have been erased. We know that the number on the ten is 1, and the number on the one is 2. We also know that if we subtract 7 from this number, we can divide it by 7, subtract 8 by 8, and subtract 9 by 9. This four digit number is 1______ ．

According to the meaning of the title, this number is a multiple of 7, 8, 9, so it is also a multiple of 7 × 8 × 9 = 504, which is 1008, 1512, 2016, 2520, etc

Four digit, thousand digit and hundred digit are dropped, ten digit is 1, one digit is 2, this number minus 7 is divided by 7, minus 8 is divided by 8, minus 9 is divided by 9?

It shows that this number can be divided by 7, 8, 9, and 7 × 8 × 9 = 504,
The end of 504 times 3 is 12
So the four digit number is 1512

In a system, the number divisible by 4 is characterized by 0,4,8 bits. What is the minimum of a?

Answer: 12
Thinking:
1. The formula from a to 10 is: Σ x × an-1 (n-1 power of a), and N is the number of digits where x is located. For example, 132 in a is converted into decimal: 1 × A2 + 3 × a + 2
2. From the meaning of the title, we know that for the number of a-Base 10, there are: 10 △ 4 = 1 × a △ 4 + 0 △ 4, more than 0, we know that a must be a multiple of 4, and because the number of bits can be 8, we know that a is greater than 8, so the minimum value of a is 12

The minimum number that can be divisible by both 6 and 12 is______ Let's break it down. The prime factor is______ ．

From the analysis, we know that the minimum number that can be divided by both 6 and 12 is 12, and the decomposition quality factor is 12 = 2 × 2 × 3, so the answer is 12, 12 = 2 × 2 × 3

Let a have 9 different divisors, B 6 different divisors and C 8 different divisors. If any two of the three divisors are not divisible, then the minimum value of the product of the three numbers is______ ．

Because a has 9 different divisors, then a is a square number, the minimum is 22 × 32 = 36B has 6 different divisors, the minimum is 22 × 3 = 12, AB does not divide each other, then B can only be 22 × 5 = 20, C has 8 different divisors, the minimum is 2 × 3 × 4 = 24, so the minimum product of three numbers is 36 × 20 × 24 = 17280

Take any two numbers from natural numbers 1 to 40. The sum of the numbers taken can be divided by 4. How many ways can we take them?

40x39 / 2 = 780 logarithm
Among 780 logarithms, 780 / 2 = 390 pairs have even sum
Among 390 pairs of even numbers, 390 / 2 = 195 pairs can be divided by 4