Missing pages!

Logic Level 2

It's a lovely evening, you are reading a newspaper in your tea time. As you go through the newspaper, you find that pages 6 and 9 are missing (your newspaper consists of 16 pages).

Considering the case above, what are the other pages which must be missing?

Details and assumptions :

  • If page 1 is missing it means, the whole sheet including the last page is missing.

  • Include pages 6 and 9 in your answer.

  • If you think the missing pages are: 1, 2, 3 and 4 provide the answer as 1 + 2 + 3 + 4 + 6 + 9 = 25 1+2+3+4+6+9=25 .

69 69 68 68 54 54 96 96

Sravanth C. by Sravanth C. , 21, India

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5 solutions

Sravanth C.
Jun 5, 2015

Newspapers always begin with page no. 1 1 , so if page no. 6 6 is missing page 5 5 must be missing too. We also know that the newspapers have a combined sheet consisting of the first two and last two pages.

So, the sheet consisting pages 5 5 and 6 6 must contain, pages 11 11 and 12 12 , you can find that by counting the pages in reverse order.

Similarly, the sheet containing page no. 9 9 must contain pages 8 8 , 7 7 and 10 10 , if you understand this properly, you will find that this sheet is the middle most one.

So, the required answer is 6 + 5 + 11 + 12 + 9 + 8 + 7 + 10 = 68 6+5+11+12+9+8+7+10=\boxed{68}

8 Helpful 0 Interesting 0 Brilliant 0 Confused

Honestly speaking , after reading this problem statement , I thought that some information was inadequate. But then I thought that if you tear one page , the number before also gets teared which led me to solve this prob. I think you must mention this fact to reduce ambiguity.

Nihar Mahajan - 6 years ago

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Oh! Okay, I'll edit that.

Sravanth C. - 6 years ago

Also did you try this ? If yes, read what I generated!

If not, generate something and do read mine!

Sravanth C. - 6 years ago

Right. It was due to that ambiguity that we removed the rating on the problem.

Calvin Lin Staff - 6 years ago
Aditya Chauhan
Jun 5, 2015

In the given newspaper the sum of the page numbers on each side of each sheet is 17(1 & 16, 2 & 15 & so on). So sum of missing page numbers = 17 times 4 which is 68

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Prashant Vashisht
Jan 14, 2019

Note that the newspaper is of 16 pages i.e. the first page is 1 and last page is 16, the second page is 2 and the second last page is 15. The pattern is that the sum of all the page numbers in 1 complete sheet is 1+2+15+16 = 34 always. This is just a simple sequence rather an A.P. with a common difference of 1. Since page 5 will be on the 3rd sheet ( along with 6,11,12) and page 9(i.e. 5th last page) will be on the 4th sheet (along with 7,8,10). So a total of two sheets are missing so the sum of missing page numbers is 34+34= 68.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

5+6+7+8+9+10+11+12 = 68

0 Helpful 0 Interesting 0 Brilliant 0 Confused

I cheated by inferring that the solution must be a multiple of 17 and the only answer that's divisible by 17 is 68. I wish this wasn't a multiple choice...

0 Helpful 0 Interesting 0 Brilliant 0 Confused

It's okay. If you've understood the logic behind the question it doesn't matter. ⌣ ¨ \huge\ddot\smile

Sravanth C. - 5 years, 11 months ago

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