Here is the explanation, showing all the steps using which I have arrived at the conclusion. Here is the order of the reindeers:
Comet is behind (Rudolph, Prancer and Cupid) ----------(1)
Blitzen is behind Cupid ------(2)
Donder is behind (Vixen, Dasher and Prancer) ------(3)
Rudolph is behind Prancer ----------(4)
Dancer is behind (Donder, Rudolph and Blitzen) --------(5)
Dasher is behind Prancer -------(6)
Donder is behind (Comet and Cupid) ------(7)
Vixen is behind (Rudolph, Prancer and Dasher) -------(8)
Blitzen is in front of (Donder, Vixen and Dancer) ---------(9)
Cupid is in front of (Comet, Blitzen and Vixen) ----------(10)
Rudolph is in front of (Donder, Dancer and Dasher) -------(11)
Vixen is in front of (Dancer and Comet) -------(12)
Prancer is in front of (Cupid, Donder and Blitzen) ---------(13)
Dasher is in front of (Vixen, Dancer and Blitzen) --------(14)
Cupid is in front of (Rudolph and Dancer) -------(15)
Here I would like to mention that as in (1), it is given that Comet is behind (Rudolph, Prancer and Cupid), I have written the names of the three within brackets because their order is not given. So it means that the three reindeers within brackets can be in any order.
Since Comet is behind Rudolph (1) and Rudolph is behind Prancer (4), we can write:
Prancer - Rudolph – Comet
Using (7) and (15) and (5), we have:
Prancer - Cupid - Rudolph - Comet - Donder - Dancer
Since Vixen is behind Rudolph (8) and in front of Comet (12), we have:
Prancer - Cupid - Rudolph - Vixen - Comet - Donder - Dancer
Also we know Rudolph is in front of Dasher (11) and Dasher is in front of Vixen (14), we now have:
Prancer - Cupid - Rudolph - Dasher - Vixen - Comet - Donder - Dancer
Since Blitzen is in font of Vixen (9) and Dasher is in front of Blitzen (14), we have:
Prancer - Cupid - Rudolph - Dasher - Blitzen - Vixen - Comet - Donder - Dancer
(Where the direction arrows ‘ X - Y’ signifies that Y is behind X or X is in front of Y).
Which is our required order of the nine reindeers.
1st: PRANCER
2nd: CUPID
3rd: RUDOLPH
4th: DASHER
5th: BLITZEN
6th: VIXEN
7th: COMET
8th: DONDER
9th: DANCER |