# Numbering of pages in the book required 2323 figures. The first two pages, the last and also the beginning of each chapter are not numbered from them. In total in the book five chapters. The first begins on the 3rd page, and the second ā on the 99th. How many pages in the book?

Makus

90

It is the algebraic sequence. formula alg. progressions such is

**a**with n+1**= a**nĀ**+ d****d = 1 since increases by 1, but it works only up to 10, at the press 10 and big figure 2 figures****and**2**= and**are necessary for 1**+ 1**to**and**to**9****= and**to 1**+ 1*9**to**and**9**=**10 further we use the same progression, d will be equal 1, but 2 figures will be printed already, we print 2 figures in an interval [10;99] then of**and**10**= and**1**+ (1*9) + (1*1)2****and**10**= 1 + 9 + 2****and**10**=12****and**99**= and**1**+ (1*9) + (1*90)2****and**99**= 190**for numbers [100;999] will spend now 3 figures, means**and**100**= and**1**+ (1*9) + (1*90)2 + (1*1)3****and**100**= 1 + 9 + 180 + 3****and**100**= 193****and**999 = and 1**+ (1*9) + (1*90)2 + (1*900)3****and**99**9****= 1 + 9 + 180 + 2700****and**999**= 27190**to us needs to find**and**x which will be equal 2323, then**2323 = 1 + 9 + 180 + 2133****2133 = 1 + 9 + 180 + (1*kh) 3****2133 = 190 + the 3rd****of the 3rd = 2133 - 190****of the 3rd = 1943****x**ā**648**Means in the book of 648 pages343

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Hariton

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