Solution: Let this book have n pages, and the torn pages are m, M+ 1 (1 =

Total pages =n*(n+ 1)/2

According to the meaning of the question:

Total pages-torn pages =20 13

Namely: n * (n+1)/2-(m+m+1) = 2013.

n*(n+ 1)/2=20 14+2m

n*(n+ 1)=4028+4m

n*(n+ 1)=4*( 1007+m)

According to the above formula, n or (n+ 1) is an integer multiple of 4, 4028+4 * 1

Meet 4028+4 * 1

n 1=63 、( n 1+ 1)=64、m 1= 1、m 1+ 1=2

n2=64 、( n2+ 1)=65、m2=33、m2+ 1=34

That is, this book * * * has 63 pages in total, with torn pages as 1 and page numbers as 1 and 2; Or this book has 64 pages, the torn page is 17, and the page numbers are 33 and 34.

According to the meaning of the title: "The middle page of this book has been torn off",

So n2=64, (n2+ 1)=65, m2=33, m2+ 1=34 is more in line with the meaning of the question.

A: This book has 64 pages.

2.

Answer: Add the remainder according to the meaning of the question.

DE: The number 1 is divided by 3, and the remainder is 1.

Divide the second number by 3, leaving 2.

Divide the third number by 3 and keep 0.

The fourth number is divided by 3, and the remainder is 2.

The fifth number is divided by 3, and the rest is 2.

When the sixth number is divided by 3, the remainder is 1.

Divide the 7th number by 3 and keep 0.

When the eighth number is divided by 3, the remainder is 1.

The ninth number divided by 3 is 1.

Divide the number 10 by 3, and the rest is 2.

The number 1 1 is divided by 3, and the remainder is 0.

At the end of the eighth number, the cycle begins with the ninth number, that is, the remainder of this series with eight numbers as the cycle number divided by three.

1998/8=249 Yu 6

That is, the number 1 998th of this series is divided by 3, and the remainder is1(corresponding to the remainder of the sixth number divided by 3).

or

1998/9=222 Yu 0

The number 1998 in this series is divided by 3, and the remainder is 1 (the remainder corresponding to the number 19 divided by 3).