Abhay, Balwinder, Chander, Danish and Eknath decided to play an innovative game. They divided a circle into 8 equal parts and numbered the parts clockwise, from 1 to 8. The conditions decided for scoring were as follows - Starting from No.1, if one moves a step clockwise, one just adds the number in the next slot to one's current number to give one one's score. If one steps anti-clockwise, one adds the number in the slot but substracts 2 from the total to get the score. Of one moves to the number diagonally across, one adds the number to he score but subtracts 3 from the total. One can't move into a slot already used.

All the replies will be appreciated.
If you give full solution, I shall be grateful, but if you are in haste, just drop a hint or cue.
Thanks in advance!

Don't we need to know where each player is on the circle? And how many moves does each get? What's the object of the game, and what sum are you looking for?

Respected Madam Joypulv!

Thanks for going through the question -

The statement is as follows -

Abhay, Balwinder, Chander, Danish and Eknath decided to play an innovative game. They divided a circle into 8 equal parts and numbered the parts clockwise, from 1 to 8. The conditions decided for scoring were as follows - Starting from No.1, if one moves a step clockwise, one just adds the number in the next slot to one's current number to give one one's score. If one steps anti-clockwise, one adds the number in the slot but substracts 2 from the total to get the score. If one moves to the number diagonally across, one adds the number to the score but substracts 3 from the total. One can't move into a slot already used.

And the questions are -
1. What is the maximum score one can have after the second move?
2. What is the minimum score one can have after the third move?
3. What is the maximum score one can have after the third move?

Sir Joypulv!


FYI Joypluv is a woman, not a man.

There are a number of assumptions you'll have to make without more information.

I'll make the assumption that A, B, C and D are on the slots in the first picture.
I'll make yet another assumption that only E is moving so that E gets the maximum points and the others not.

The first picture is the initial (completely random, except for E who is placed on the highest number minus two turns).

http://p1cture.it/images/eb9c3ab20b1286f763ed.png

Turn 1:
B moves to 2, gets penalised 2 points, getting 3 points net.
C moves to 3 (which is now free), getting 3 points and gets penalized 2 points, getting 4 points net.
D moves to 4 (which is now free), getting 4 points and gets penalized 2 points, getting 7 points net.
E moves to 7, getting 13 points net.
A moves to 1, getting 9 points net.

Turn 2:
A moves to 5, getting 14 points net.
B moves to 1, getting 1 point and losing 2 points, for a total of 2 points.
C moves to 4, getting 4 points, hence 8 points.
D moves to 2, getting 2 points and penalised 3 points, for a total of 6 points.
E moves to 8, getting 8 points for a total of 21 points.

FYI Joypluv is a woman, not a man.


I get very frustrated when people change their posts to conform to the answers.