"Draw a row of spaces on a piece of paper, and each * * has 100 spaces. Write a natural number in each space, so that the sum of the numbers in every seven adjacent cells is 35. It is known that 12 is 8, 37 is 12, 48 is 4, and 57 is 5, so the sum of all natural numbers in this 100 grid is (? )"
According to the recognition result, a row of spaces is simulated with columns in Excel table, and the sum of all natural numbers in this 100 space is (507).
The detailed calculation process is as follows:
Detailed calculation flow chart
Detailed description of the calculation process:
From line 57, fill in alphabetically ...) Line by line (cells with numbers are not filled), and then calculate according to the sum of seven adjacent numbers =35:
For example, the sum of seven adjacent numbers in line 57 =? 5+a+b+c+d+e+f=35
The sum of seven adjacent numbers in line 58 = a+b+c+d+e+f+g=35.
From the difference between the above two formulas, we can get: g=5?
Other lines and so on, and finally get "5? □ 4 □□□□□□□12 "permutation cycle, and the sum of the natural numbers of these seven cells =35.
Because: 100 ÷ 7 = 14...2
So: 100 unit has 14 7 units +2 units.
By the 57th grid, there should be eight 7 grids+1 grids, and the first grid should be 5.
Starting from the 58th grid, there should be 6 grids of 7+1, and the100th grid should be 12.
So the sum of these 100 natural numbers = 35x14+5+12 = 490+17 = 507.