Christmas Trivia

As this week’s newsletter falls on Christmas, I can’t help but do Christmas trivia. However, after four newsletters on that topic, I have run out of questions. So, I hope you won’t mind if I republish my questions from the December 26, 2019 newsletter. However, before we get to that, I do have a fresh logic puzzle.

Logic Puzzle

On Monday there are three boy babies in a hospital nursery and an unknown number of girls.

On Tuesday a new baby is added.

On Wednesday a baby is selected at random, which is a boy.

What is the probability the baby born on Tuesday was a boy?

Answer at the end of the newsletter.

Christmas Trivia Questions

1. What made Frosty the Snowman come to life?
2. What spy reports to Santa Claus to help him keep track of who has been naughty and nice?
3. What Christmas staple was originally meant to help us remember the shepherds who visited Jesus in the manger?
4. Who was Rudolph the Red-Nosed Reindeer's elf companion?
5. In what holiday movie does Donald Trump make a cameo appearance?
6. In which country does the advent calendar come from?
7. Who is the legend of Santa Claus based on?
8. The song Deck the Halls contains the lyric, "Troll the ancient Yuletide carol." What does Yuletide mean?
9. What is the modern image of Santa Claus based on?
10. On what date does the Armenian Apostolic Church celebrate Christmas?

 

Christmas Trivia Answers

1. A silk hat
2. The elf on a shelf
3. A candy cane, because they are shaped like a shepherd's hook
4. Hermey
5. Home Alone 2
6. Germany
7. Saint Nicholas, a Greek bishop who was said to be very generous with gifts. More information is available on Wikipedia
8. Yule/Yuletide is an ancient Norse pagan winter festival lasting about two months. It seems to be have been mainly celebrated in what is present day Germany. The name "Yule" is attributed to a Norse month by that name. More information is available on Wikipedia
9. The first known image of Santa Claus is by political cartoonist Thomas Nast, who drew the image for an 1863 issue of Harper's Weekly. (see image above)
10. January 7

 

Logic Puzzle Answer

The answer is 4/7.

Before I get to the answer, I ask a similar yet easier version of this problem last week in my December 18, 2025 newsletter. If you haven’t done that one first, I recommend doing so before you tackle this more difficult puzzle.

Short Solution

Let's call the number of girls in the nursery on Monday g.

There are two possible explanations for what happened. Let's call them x and y.

x = Boy added on Tuesday and a boy is observed on Wednesday. The probability of this is (1/2)*(4/(g+1)).

y = Girl added on Tuesday and a boy is observed on Wednesday. The probability of this is (1/2)*(3/(g+1)).

x+y = (1/2)*(4/(g+1)) + (1/2)*(3/(g+1)) = 3.5/(g+1).

The question is asking what is the probability of the two, x is what happened. This would be

x/(x+y) =

(1/2)*(4/(g+1)) / 3.5/(g+1) =

(1/2)*(4/(g+1)) * ((g+1/3.5) =

(1/2)*(4/3.5) = 2/3.5 = 4/7

Formal Solution

The Bayesian conditional probability formula says that Prob(X given Y) = Prob(X and Y)/Prob(Y), where prob(x)=probability of any event x. Let's let:

X = Boy added on Tuesday

Y = Boy observed on Wednesday

In this case:

Prob(X given Y) = Prob(Boy added on Tuesday given boy observed on Wednesday) = Prob(Boy added on Tuesday and boy observed on Wednesday)/Prob(Boy observed on Wednesday).

Let's let G = number of girls on Monday.

Given no information about the draw, the probability any new addition to the nursery is a boy is 50%.

If the Tuesday baby is a boy, the probability a boy is observed on Wednesday is 4/(G+4).

If the Tuesday baby is a girl, the probability a boy is observed on Wednesday is 3/(G+4).

Prob(Boy added on Tuesday and boy observed on Wednesday) = (1/2)*(4/(G+4)) = 4/(8+2G)

Prob(Boy observed on Wednesday) = (1/2)*(4/(G+4)) + (1/2)*(3/(G+4)) = 7/(8+2G)

Using the The Bayesian conditional probability formula, the answer is:

(4/(8+2G)) / (7/(8+2G)) = 4/7