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Some mathematical problems ...
1, 777=770+7, only 7 of the single digits are affected, so it is the same as 7,777 single digits.

And 71= 7,72 = 49,73 = 343,74 = 2401,7 5 = 16807.

It can be seen that the unit numbers are: 7, 9, 3, 1, 7 ... Every fourth power cycle, 777= 194*4+ 1.

So 7 777 is the same as 7 1 digit, and 7 1 = 7, so the result is 7.

2. The principle is the same as above, and the 9 n law is 9, 1, 9, 1...2 cycles. 123456789 divided by 2 equals 1.

So, like 9 1 = 9, the answer is 9.

To find a number, just add all the numbers in the formula. The corresponding single digits of each item are as follows:

1! —— 1,2! ——2,3! ——6,4! ——4,5! ——0

Starting from 6, because the unit is 0 * n = 0(n >;; 5)

Add it all up: 1+2+6+4+0+0 = 12, so the result is 2.

4. The power of 100 1 3 is the method of problem 1, and the unit number is 3, 9, 7, 1, 3 ...1001-20.

The power of 17 of 1002 is 7, 9, 3, 1, 7... 1002- 1000 = 2, and the result is 9;

The power of 19 of 1003 is 9, 1, 9, 1, ...1003-1002 =1,and the result is 9;

1×9×9=8 1, so the total result is 1.

The answers to questions 1 to 4 are as follows:

1、7

2、9

3、2

4、 1