Advent Brain Teasers, Logic Puzzles, and Math Problems
What can I say? I love Christmastime, and I also love learning, puzzles, and math. So, how might I be able to mix those together? A puzzle per day to keep us all thinking as Christmas approaches.
The days leading up to Christmas in the Christian tradition are known as the advent season. The word advent means "arrival" and it helps Christians to look towards and focus their hearts and minds on the arrival of Jesus. The themes to help us reflect on this time are: hope, peace, love and joy. While you may not celebrate Christmas, I wish you all a season of hope, peace, love and joy.... and some fun problem solving too!
I hope that these riddles, problems, codes, puzzles and brainteasers provide another useful and fun resource for you and your family. My target age for these problems is for 4th graders to be able to complete them independently, but still accessible for 2nd-3rd graders as well, perhaps with some support. There are differing levels per day, with some variation as different skills are involved. I encourage you to be sure to ask your child to explain or to show their thinking.
Happy puzzling together as a family!
Day 1: Puzzling Patterns 🎁
Additional Challenge: Is there an equation or formula you could create to always know which color the paper would be?
🔍 Answers
Question 1: Gold (12 ÷ 3 = 4, and gold is the 3rd color in each set).
Question 2: Green (The closest multiple of 3 is 30, and 29 is one less than 30. 30 ÷ 3 = 10, and gold is the 3rd color in each set. The color just before gold is green).
Question 3: Answers will vary.
Day 2: Reindeer Name Mix-Up! 🦌
Hint: Here are the names of Santa's reindeer: Dasher, Dancer, Prancer, Vixen, Comet, Cupid, Donner, Blitzen, and Rudolph.
Remember only one of the names can be reshuffled to create a new word. Have fun!
For an additional challenge, find the average number of letters in the reindeers' names.
🔍 Answers
Mixed up Names: Dasher becomes Shared
The average number of letters in a reindeer’s name is 6. 🎄✨ 6+6+7+5+5+5+6+7+7=54 letters in total. 54÷9=6 letters
Day 3: Christmas Tree Puzzler🎄
What's happening on this tree? What is the relationship between the numbers? What patterns do you notice? What are the missing numbers?
🔍 Answers
Going from top to bottom, left to right: Star = 1, 4, 2, 11, 12
The pattern is that one of the numbers is subtracted from the number beside it to give you the number above it.
Day 4: Too Many Gifts! 🎁
For example, on Day 3 you would be given the three French hens, plus two more turtle doves AND a partridge in a pear tree.
Just a reminder regarding all the different days:
- 1st Day: A partridge in a pear tree
- 2nd Day: Two turtle doves
- 3rd Day: Three French hens
- 4th Day: Four calling birds
- 5th Day: Five golden rings
- 6th Day: Six geese a-laying
- 7th Day: Seven swans a-swimming
- 8th Day: Eight maids a-milking
- 9th Day: Nine ladies dancing
- 10th Day: Ten lords a-leaping
- 11th Day: Eleven pipers piping
- 12th Day: Twelve drummers drumming
Hint: You might want to calculate the gifts given per day, including the previous days gifts (again) then find the final sum.
🔍 Answer
On each day, you receive the gifts for that day plus all the previous gifts from earlier days. This is the sum of the first n numbers repeated for each day:
Gifts on Day 1: 1
Gifts on Day 2: 1+2=3
Gifts on Day 3: 1+2+3=6
Gifts on Day 4: 1+2+3+4=10
You get the idea and the pattern.
Once you solve for each day, then you need to add all of those together.
1+3+6+10+15+21+28+36+45+55+66+78=364
The total number of gifts received over all 12 days of Christmas is 364 gifts.
Fun fact: That’s one gift for almost every day of the year! 🎄✨
Day 5: Snowflake Intricacies ❄️
Hints:
The central hexagon always counts as 1. The first layer adds 6 hexagons. Notice the pattern in how many hexagons are added for each new layer.
🔍 Answer
- Layer 0 (Center): 1 hexagon.
- Layer 1: Adds 6 hexagons, total = 1+6=7
- Layer 2: Adds 12 hexagons, total = 7+12=19
- Layer 3: Adds 18 hexagons, total = 19+18=37
Total after 3 layers: 37 hexagons.
Extra Challenge: Can you create a formula for any number of layers?
Fun Fact: Did you know that all snowflakes are hexagonal, meaning they have six sides? This is due to the way water molecules naturally arrange themselves when freezing into ice crystals, forming a hexagonal structure at the molecular level; this is why every snowflake, regardless of its intricate design, will always have six sides.
Day 6: What's a Snowman Worth? ⛄️
🔍 Answers
Snowman is worth 36, Snowflake is worth 12
Substitute the 3 snowflakes in the place of the snowman and then you have 4 snowflakes being equal to 48. Divide 48 by 4 and you get the 12 per snowflake, then you can solve for the snowman.
Day 7: How Efficient is Santa? 🎅🏼
Santa is delivering presents, and he’s come to a community of 30 homes. Each house has stockings hanging by the fireplace, but the number of stockings varies:
- 10 homes have 3 stockings each.
- 10 homes have 4 stockings each.
- 10 homes have 5 stockings each.
Rules for Santa’s Delivery:
- Sliding down the chimney: It takes Santa exactly 5 seconds to slide down the chimney into each house.
- Filling stockings: Santa needs 2 seconds to fill each stocking with goodies.
- Travel time between houses: It takes Santa 1 minute (60 seconds) to travel from one house to the next.
How long will it take Santa to complete all his deliveries?
🔍 Answers
Step 1: Time per house
- Sliding down the chimney: 5 seconds per house.
- Filling stockings:
- For houses with 3 stockings: 3×2=6 seconds
- For houses with 4 stockings: 4×2=8 seconds
- For houses with 5 stockings: 5×2=10 seconds
- Total time per house:
- 3 stockings: 5+6=11 seconds
- 4 stockings: 5+8=13 seconds
- 5 stockings: 5+10=15 seconds
Step 2: Time for all houses (sliding and filling only):
- 10 homes with 3 stockings:10×11=110 seconds
- 10 homes with 4 stockings:10×13=130 seconds
- 10 homes with 5 stockings:10×15=150 seconds
- Total time for all 30 houses (sliding and filling):110+130+150=390 seconds
Step 3: Travel time between houses
- Santa travels 29 times between the 30 houses: 29×60=1,740 seconds
Step 4: Total time for the community
- Add the time for sliding and filling to the travel time: 390+1,740=2,130 seconds
Convert to minutes:
2,130÷60=35.5 minutes
Day 8: Snow Flurry Frenzy ❄️❄️❄️
As an added challenge, if there were to be a missing number in the center of the snowflake, what would it be?
🔍 Answers
The outermost parts are the prime factors of the number they are connected to. From top to bottom: 5, 12, 20, 2.
Challenge: Multiply all the innermost numbers and you'll get a product of 69,984,000.
Day 9: Sleigh Troubles 🛷
In case you've never done a magic square puzzle before, the rules are to use the numbers 1-9 (when it's a 3x3 square, unless other numbers are stipulated), with no numbers being repeated.
🔍 Answers
[ 8 ] [ 1 ] [ 6 ]
[ 3 ] [ 5 ] [ 7 ]
[ 4 ] [ 9 ] [ 2 ]
The elves need to input the numbers, 4, 3, 7, and 9 to unlock the barn door. Thanks for helping them! 🎁✨
Day 10: Letter to Santa 💌
🔍 Answer
The message was a reverse code with all letters and the entire message being flipped. Start at the bottom as work your way backwards towards the top. It says:
Dear Santa,
Hello, hope you are well. I would like a toy airplane and a tablet please. Thank you!
Benny
Day 11: Holiday Budget Mishap 💵
🔍 Answer
It should be: 489 + 18, plus 236 +25 = $768.
Day 12: Cookie Conundrum 🍪
🔍 Answer
Answer:
Plate 1: 12 - 3 = 9
Plate 2: 12 ÷ 2 = 6; 6 − 3 = 3
Plate 3: 6 + 6 = 12; 12 − 3 =9
Total: 9 + 3 + 9 = 21 cookies
Day 13: Triangular Tree 🎄
🔍 Answer
I found 24... anyone else find more? Let me know in the comments.
Day 14: Sweater Weather 🧥
🔍 Answer
You could make a chart, table or a tree diagram, but it in the end it comes down to: 3 × 3 × 3 = 27 combinations
Day 15: Holiday Einstein-Style Riddle 🏠
Inspired by Einstein's Riddle, here are all the clues and information for this holiday themed riddle:
In case it's easier to have a print out, don't worry I have that for you! Click below for the free download. Happy solving!
🔍 Answer
If you're more visual, please see the grid below this drop down box.
- Alex lives in the red house, received the toy train, baked sugar cookies, and decorated with a snowman.
- Bella lives in the white house, received the stuffed reindeer, baked gingerbread cookies, and decorated with the nativity scene.
- Dani lives in the blue house, received the book, baked hot cocoa, and decorated with string lights.
- Charlie lives in the green house, received the puzzle, baked fruitcake, and decorated with a wreath.
- Eli lives in the yellow house, received the Christmas sweater, baked peppermint bark, and decorated with garland.
Here's another way to see or organize your results. I always feel like putting it in a grid makes the most sense.
Day 16: Sum Snow ❄️
🔍 Answer
8251 + 473 = 8724 (could be more than one right answer.)
Day 17: Sudoku the Holidays 🧩
🔍 Answer
Row 1: Star, gingerbread, gift, holly
Row 2: Gift, holly, gingerbread, star
Row 3: Gingerbread, star, holly, gift
Row 4: Holly, gift, star, gingerbread
Day 18: Magical Tree Triangles 🎄
🔍 Answer
Sides (can be interchangeable in terms of the side, just need the same shared vertex):
Side 1: 1, 6, 7 and 3
Side 2: 3, 8, 4 and 2
Side 3: 2, 5, 9 and 1
Day 19: Ornament Identification ✨
🔍 Answer
96 is the number that fits all the categories.
Day 20: Tangled Lights 🎄
🔍 Answer
Yellow = 11
Green = 2
Red = 3
Final answer: 19
Day 21: Matchstick Puzzler
🔍 Answer
You are trying to literally spell the word TREE. Remove the sides or bottoms sticks as needed to spell the word TREE.
Day 22: Another Snowflake Number puzzle ❄️
🔍 Answer
The missing number is 17. You take the numbers on the opposite side and add them together.
3 + 14 = 17
This is true of the others as well, 5 + 7 = 12, 9+6 = 15, and 4 + 10 = 14
Day 23: Nutcracker Ballet Times 🩰
🔍 Answer
- Act 1 transitions:
There are 8 transitions between the 9 dances (no transition after the last dance). 8 × 30 = 240 seconds = 4 minutes. - Act 2 transitions:
There are 13 transitions between the 14 dances. 13 × 30 = 390 seconds = 6.5 minutes. - Total transition time: 4 + 6.5 = 10.5 minutes.
- The intermission adds 20 minutes.
Total Time Calculations:
- Act 1: 50 minutes + 4 minutes (transitions).
- Act 2: 40 minutes + 6.5 minutes (transitions).
- Total performance time: 50 + 4 + 40 + 6.5 = 100.5 minutes.
- Include intermission: 100.5 + 20 = 120.5 minutes, or 2 hours and 30 seconds.
Day 24: A Secret Christmas Message 👪🏼
🔍 Answer
Each letter in the alphabet is replaced with the opposite... A = Z etc.
Instead of abcdefghijklmnopqrstuvwxyz each of these maps to: zyxwvutsrqponmlkjihgfedcba
Based upon that, the message is: Jesus is born!
Merry Christmas everyone!
Hope you enjoyed all of these riddles, problems and brainteasers! For more like this and access to even more math-related content, be sure to sign up for Raising Mathematicians!
Have a very Happy Holiday and a Happy New Year!