Analysis:
1), and it must be a continuous number.
Gauss's story reveals the addition of continuous numbers:1+2+3+100 =101x 50 = 5050.
2) A book is torn from the middle, and the sum of the remaining page numbers is exactly 1000.
It can be seen that the total number of pages is less than 50 because1+2+3 ...+50 = 51x25 =1275.
3)1275-50-49-48-47-46 =1035
4) The extra 35 must be the sum of torn pages, so (35- 1)÷2 = 17 pages, 17+ 18 = 35.
Check:
The sum of 45 page numbers is 1+2+3+45 = 1035.
1035 - 17 - 18 = 1000
You can also use equations, but I don't seem to have learned binary linear equations in the fifth grade, but I'll list them for you.
Let the sum of page numbers be x and the number of page numbers be y, and the formula is: (y+1) * y/2 = x.
Y=44, x=990, less than 1000, if the condition is not met, it will be removed;
Y=45, x= 1035, and the sum of the two page numbers is 35, which are 17 and 18 respectively, satisfying the conditions.
Y=46, x= 108 1, and the sum of the two pages is 8 1, 40,41respectively. Generally, the number of pages on the same piece of paper is odd first and then even. If it does not meet the requirements, it will be removed.
Y=47, x= 1 128, and the sum of the two page numbers is 128. No matter which page number adds up, it is not satisfactory. Remove it.
As you can see, this book has 1035 pages, and the torn pages are 17 and 18 pages respectively.
Write your own answers.
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