# Puzzle 17) Vivek and Alphabetical order

Submitted by Amit Shukla, on August 14, 2017

Puzzle

A boy named Vivek is interested in solving alphabetical puzzles. He refers many different book in search of puzzle regarding alphabets. One day he found a unique puzzle based on alphabetical order. In the puzzle all the capital letters of the English alphabet from A to Z followed by the lower case letter from ‘a’ to ‘z’ are placed one in each slot, in 52 slots around a circle in clockwise direction. All the slots are counted in the clockwise direction starting with the slot containing A, and the letter in every fifth slot is removed. Now he has to find out that how many more slots will have letters left in them immediately after ‘m’ is removed from its slot?

Important points of puzzle:

1. Vivek is interested in solving puzzle based on alphabetical order.
2. One day he found a unique puzzle.
3. According to puzzle all capital letter of English alphabet from A to Z followed by the lower case letter from ‘a’ to ‘z’ are placed one in each slot.
4. There are total 52 slots around the circle.
5. All the slots are counted in the clockwise direction starting with the slot containing A.
6. The letter in every fifth slot is removed.
7. Now he has to find out that how many more slots will have letters left in them immediately after ‘m’ is removed from its slot?

13

Reason

There will totally be 52 letters out of which ‘m’ is the 39th letter. If we count from A, in the first round the letter removed will be those positioned in the slots of.
5, 10, 15……………………50, 10 letters, then
3, 8, 13……………………48, 10 letters, then
1, 6, 11………………………. 51, 11 letters, then
4, 9, 14, 19, 24, 29, 34 – 7 letters before 39 total number of letter struck off is 10 + 10 +11 + 7 = 38 letters before 39 fi 50, m is the 39th letter to be removed.
So, 13 letters are left in their slots. Hence the answer is 13.