There are n natural numbers added: 1 + 2 + 3 + 4 + +N = AAA (and exactly three digits of the same number), so what is n equal to?

n(n+1)/2=a*111
N (n + 1) = a * 2 * 3 * 37, a is 1 ~ 9
One of N and N + 1 is a multiple of 37. If n = 37k, then 37k ^ 2 + k = 6a ≤ 54, so k = 1, then a is not an integer. If n + 1 = 37k, then 37k ^ 2-k = 6A. Similarly, K can only be taken as 1, then a = 6
So n = 36

Make six eights into several numbers (one digit or two digits) so that the sum of multiplication and addition is equal to 800

Think like this: first use four 888 + 88 = 176, 800-176 = 624, the remaining two 8 cannot get 624, first use three 88 * 8 * 8 = 512, 800-512 = 288, the remaining three 8 cannot get 2888 * 8 + 8 = 72, 800-72 = 728, the remaining three 8 cannot get 728.8 * 88 = 704, 800-704 = 96, 8 + 88 = 96, so 88 * 8 + 88 + 8 = 800

Six eights make up several numbers, so that the sum of each phase is equal to 800

88×8+88+8=800

There are three different numbers, which can make up six different three digit numbers. The sum of them is 3330. What is the smallest three digit number?

Answer: 159
Let these three numbers be a, B and C. according to the principle of permutation and combination, only when these three numbers are different can they be arranged into six three digit numbers, and a, B and C appear twice in the hundred, ten and individual digits of the three digit numbers
So there is the equation:
(100+10+1)(2A+2B+2C)=3330
So a + B + C = 15
After that, because a, B and C are not equal, it can be seen from simple logical reasoning that the three numbers are any combination of 1 to 9, but they must be added up to 15. According to simple enumeration, they are 1 + 5 + 9 = 15
Thus, the minimum three digit number is 159

There are three numbers, which can make up six different three digit numbers. The sum of them is 3330, and the biggest one is ()

Let three numbers be a, B and C, then the six different three digit numbers are ABC, ACB, BAC, BCA, cab and CBA. The above six numbers are different three digit numbers, so a, B and C are not zero, and they are different numbers. The sum of these six numbers is: 2 * (a + B + C) + 20 * (a + B + C) + 200 * (a + B + C) = 3330

Three different numbers can make up six different three digit numbers. The sum is 3330. Find the smallest three digit number
I want answers and rules

Three numbers are a, B, C, so the six different three digits are
100a+10b+c
100a+10c+b
100b+10a+c
100b+10c+a
100c+10a+b
100c+10b+a
All of the above add up to 3330, so
222 (a + B + C) = 3330, then
a+b+c=15
The smallest three digit number is 159 when a = 1, C = 9, B = 5

Six different three digit numbers are composed of three different numbers a, B and C. The sum of them is equal to 4440. What is the largest number?

The sum of six numbers is 222 (a + B + C) = 4440
a+b+c=20
9+8+3=20
So the maximum is 983

Six different three digit numbers are composed of three different numbers a, B and C. The sum of them is equal to 4440. What is the largest number?

Let these three numbers be a, B, C, then the three digits are 100A + 10B + C, 100A + 10C + B, 100b + 10A + C, 100b + 10C + A, 100C + 10A + B, 100C + 10B + a. the sum of them is 222a + 222b + 222c = 4440, so there is a + B + C = 20. In the case of a ≠ B ≠ C, there are: A, B, C are (8,7,5), (9,6,5), (9,7,4) and (9,8,3) respectively. In these four groups of numbers, the maximum number that can be composed is 983

Fill the nine numbers - 2, - 1, 0, 1, 2, 3, 4, 5 and 6 into the nine spaces of the square matrix, so that the sum of the three numbers in the horizontal, vertical and diagonal angles is 6

As shown in the figure

Fill the nine numbers - 6, - 5, - 4, - 3, - 2, - 1,0,1,2 in the nine spaces of the matrix in the figure below, so that the three numbers of each row, column and diagonal are added
And are equal!

-6-5-4-3-2-1+0+1+2=-18
-18÷9=-2
The average sum of three numbers in each row, column and diagonal = - 2 × 3 = - 6
∴
-1 0 -5
-6 -2 2
1 -4 -3

There are n natural numbers added: 1 + 2 + 3 + 4 + +N = AAA (and exactly three digits of the same number), so what is n equal to?