**Merry Christmas!**

**Throughout the month, to accompany the release of our book on the Mathematics of Christmas, Hannah Fry & I were tweeting out Christmathsy bits and pieces, one a day, advent calendar style.**

Thanks for following the Indisputable Santa Mathematical Advent Calendar. Just a few loose ends to wrap up, with a solution to our Christmas Eve puzzle today, with the solution to Friday’s puzzle (Santa’s Dressing Room Disasters) to come tomorrow…

**CLICK HERE TO SEE THE WHOLE CALENDAR**

**SOLUTIONS TO PREVIOUS PUZZLES**

**Click here for Saturday’s puzzle.**

Scroll down for the solution…

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**Solution to Day 24**

Let’s number the clues, to make things simpler:

**1.** Only the front pair contains two reindeer with the same first initial.

**2. **Cupid is further forward than Dasher.

**3. **There is exactly one full row between Comet and Blitzen.

**4. **Prancer is immediately in front of Vixen (nose to tail).

**5. **Donner is on the same side of the formation as Dasher, but on the opposite side to Dancer.

**6. **At least one pair of reindeer whose names are listed consecutively in “The Night Before

**6. **Christmas” are side by side.

**7. **Fewer than half the four pairs of reindeer are arranged with their two names in alphabetical

**7. **order (if Santa looks from left to right).

From **1**, we know that the front pair are either Comet & Cupid or two of Dasher, Dancer and Donner. However, **2** excludes Dasher. In fact, we can also exclude Comet & Cupid. If they formed the front pair, then **3** implies that Blitzen is in the third row, but then, once you have fitted in Prancer and Vixen nose to tail (**4**), there is no way to place Dasher, Dancer and Donner without two of them being side by side, which would violate **1**. Therefore, **the front pair is Donner and Dancer.**

Now consider **6**. Which pairs of reindeer from the poem could be side by side? Not Dasher and Dancer or Dancer and Prancer, since we’ve already established that Dancer forms a pair with Donner. Not Prancer and Vixen either (by **4**). Vixen and Comet is a possibility, but Comet and Cupid is not (by **1**). Finally, Cupid and Donner and Donner and Blitzen are impossible, again because Donner has already been paired with Dancer. Therefore, to fulfil **6**, **Vixen and Comet must be side by side.**

Now, since the first row is occupied, **4** implies that Vixen is not in the second row. Also, **3** implies that Comet is not in the third row, and since they are side by side, **Vixen and Comet make up the back row.** This also means that (by **3**)** Blitzen is in the second row** and (by **4**) **Prancer is in the third row, immediately in front of Vixen.** There are two spaces left, in the second and third rows, and by **2 **(and **5**), **Cupid must be in the second row, with Dasher in the third row (on the same side as Donner).**

So, we know that the rows are: **Donner and Dancer, Blitzen and Cupid, Dasher and Prancer, Vixen and Comet. **We also know that **Donner, Dasher and Comet (call them Group 1)**** are on one side, with Dancer, Prancer and Vixen (Group 2) on the other.** We don’t know which of these groups Blitzen and Cupid fit into though.

All this has whittled the possible arrangements down to just four:

- LEFT: Group 1 + Blitzen, RIGHT: Group 2 + Cupid;
- LEFT: Group 1 + Cupid, RIGHT: Group 2 + Blitzen;
- LEFT: Group 2 + Blitzen, RIGHT: Group 1 + Cupid;
- LEFT: Group 2 + Cupid, RIGHT: Group 1 + Blitzen.

Based on everything we’ve learnt, only the final option fits with clue **7** (with Dancer and Donner as the only pair in alphabetical order). Therefore, the true arrangement is:

**Dancer , Donner**

**Cupid , Blitzen**

**Prancer, Dasher**

**Vixen, Comet
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**Santa in his Sleigh**

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Correct answers, this time, came from Olaf Doschke, Troy ToTheWorld, PRL & Catherine Evans. We asked Santa to leave an extra satsuma in your stockings.