Page numbers of a book-Rejoinder

There has been no response so far.
However the solution can be arrived at as follows-
If there were 63 pages in the book,the sum of the page numbers from 1 to 63 will be 2016.
As the addition of an extra page number gave the total 2014,the total number of pages could not be 63 but 62.
For 62 pages the sum of the page numbers will be 1953 and so the page number added wrongly should be 2014-1953=61. 

Security passwords/numbers

Here is a puzzle regarding security code-
Before the entry gate of a secured post,the security guard will give a password to the person wishing to enter.The person has to give a reply.Only if the reply is correct he will be allowed to enter.
Person A comes to the gate.The guard mentions the number 12,A gives the answer 6. He is allowed to enter.
Person B comes to the gate-The guard mentions 6.B gives the answer 3.He is allowed to enter.
Person C comes to the gate after seeing the previous 2 persons entering.The guard mentions 8.C gives the reply 4.He is not allowed inside.
Can you make out why?
The code followed is this-When the guard gives a number,the person wishing to enter should find out the number of alphabets required for writing out the number and give it as the answer-6 letters for 12 and 3 letters for 6. You can see that for the number 8,it should be 5 instead of 4 due to which C was not allowed inside.

Page numbers of a book

A puzzle from Monday Edex issue (New Indian Express) of  9 june 2014-
The pages of a book are numbered 1 to n.When the page numbers were added by someone just for fun,one of the page numbers were added twice,resulting in an incorrect sum of 2014.Find the page number which was wrongly added twice..

Date of death-paradox

See the paradox below-
Both great writers Shakespeare and Cervantes died on the same date 23 April 1616.However they also died 10 days apart.How?
Here is the explanation-
Shakespeare died on 23 april 1616 according to Julian Calendar which was still used in England at the time whereas Cervantes died on 23 april 1616 according to the Gregarian calendar which was used in Madrid.The difference between the calendar accounts for the paradox.Spain had opted for Gregarian calendar as early as in 1582,while England waited till1752 to effect the change.

Who won what medals-Logic puzzle

Students of a school are divided into 3 teams-A,B and C
Using the clues given below,work out the number of gold,silver and bronze medals that A,B and C-
won-
1)A won 1 gold medal more than B,but 3 silver medals less than B
2)C has the highest number of bronze medals(18),but least number of gold medals(7)
3)Each team won at least 6 medals each type
4)B won  2 bronze medals more than gold medals
5)The 3 teams won 38 bronze medals in total
6)B won 27 medals in total
7)C won twice as many silver medals as the number of gold medals that B won

A number sequence to be filled-Rejoinder

I had asked readers to find the next number in the sequence 10,9,60,90,70,66
I had also suggested to treat this as an alpha-numeric sequence .
The numbers given are the number of alphabets which are required for expressing the highest numbers with  3,4,5,6,7,and 8 alphabets.
You are thus required to find the highest number which needs 9 alphabets for expression.
No one has given a solution.
Obviously the highest number has to be below 100.
Let us first consider numbers from 90 to 99.
97,98 and 99 require more than 9 alphabets.Only the number 96 requires 9 alphabets and so this is our candidate.  

Trilemmas

The term trilemma is similar to the term dilemma.
It refers to 3 choices/statements available out of which only two can be seen as true or amenable to acceptance
There are many examples-I have shown 2 of them below-
1)Manufacturing processes-Choices available-Fast...Good....Cheap
2)Three statements regarding religious beliefs
a)If god is unable to prevent evil,then he is not very powerful
b)If god is not willing to prevent evil then he is not at all good
c)If god is both willing and able to prevent evil then why does it(evil) exist?