This Christmas, due to the lingering effects of the recession, along with the rise of easy online shopping options like Amazon and Best Buy, Santa Claus has been forced to cut costs to remain competitive. He has outsourced gift production to India (largely due to the high demands of the Elves Union), and has downsized his reindeer squad to 7: Blitzen, Cupid, Dasher, Komet, Prancer, Vixen, and, of course, Rudolph. With only 7 reindeer pulling his sleigh, however, ensuring the optimal order of the reindeer is essential for flight. Help Santa save Christmas by figuring out the best reindeer order for his sleigh with the following restrictions:

• Each reindeer must be assigned a position pulling the sleigh, and each reindeer can only be assigned one position, 1 through 7

• Rudolph must be fourth, or he must be somewhere in between Dasher and Prancer, but not both

• Prancer must be before Cupid

• Either Vixen or Blitzen must be 3rd

• If Vixen is before Rudolph, then Prancer must be before Dasher, otherwise, Komet must be before Vixen

**• Cupid may not be immediately before Komet, or immediately after Dasher
**

*1.*If Dasher is first, then which one of the following must be true?

a. Rudolph is 4th

b. Komet is 5th

c. Rudolph is 2nd

d. Blitzen is 3rd

e. Cupid is 6th

*2.* If Rudolph is 5th, then which one of the following could be true?

a. Cupid is 7th

b. Vixen is 2nd and Prancer is 4th

c. Prancer is 2nd and Blitzen is 4th

d. Dasher is 1st

e. Dasher is 7th

(Note: The following questions do not have answer choices; this is to prevent you from just plugging and chugging your way through the answers, instead you should do work up front. Try and work through the deductions and you should be able to anticipate the answer)

*3.* If Rudolph is 4th and Blitzen is 5th, then for how many of the reindeer can their exact spot be determined?

*4.* If Komet is 7th, then how many different reindeer can be 6th?

*5.* If Prancer is 5th, then how many spots can Dasher be assigned to?

*6.* If Dasher is 4th, then Komet must be assigned to which position?

*Bonus:* Assigning which reindeer to which spot will determine the exact spot of Dasher? (and no, you may not just assign Dasher)

*(Answers: 1: d; 2: e; 3: All seven; 4: Two (Blitzen & Dasher); 5: Two (1st & 7th); 6: Fifth; Bonus: Rudolph 6th)*

What a fun game.. perhaps it’s too late to ask, but I got stuck on #1, and I think it’s because I misunderstood rule #5:

“If Vixen is before Rudolph, then Prancer must be before Dasher, otherwise, Komet must be before Vixen”

I took it as if V-R then P-D or K-V.

But is it actually if V-R then P-D or if R-V then K-V

???

Thank you for your help..If I understood the rule correctly, could you kindly explain why d is correct..? Couldn’t it be D-R-V-K-P-C-B?

Yes, it’s a very tricky rule but your second representation is correct. This rule is actually two conditional rules: If V – R, then P – D; if R – V, then K – V. So which rule we can employ depends on whether V is before or after R.

So the order D – R – V – K – P – C – B would violate that rule because R is before V, so K must be before V too.

Nick I get what you mean about tricky rules now. I liked this game, even though I did it wayyy after XMAS =)

Glad to hear it. I tried to pull out all stops with the rules