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Christmas card 2025
2025-12-04
As usual, I spent some time this November,
designing this year's Chalkdust puzzle Christmas card
(with help from TD and Jacob).
![](javascript:showlimage("card2025.jpg"))
The card contains 12 puzzles: 8 in the green section, and 4 in the red or yellow section. By colouring the two squares on the front of the card containing every pair of digits in each answer
(eg if an answer in the green section were 3305, you would colour the squares containing 33, 30 and 05 green), you will reveal a Christmas
themed picture.
If you're in the UK and want some copies of the card to send to your maths-loving friends, you can order them from my Ko-Fi shop.
If you want to try the card yourself, you can download this printable A4 pdf. Alternatively, you can find the puzzles below and type the answers in the boxes. The answers will automatically be used to colour in the appropriate squares.
Green | ||
| 1. | What is the sum of all the odd integers between 0 and 12? | Answer |
| 2. | What is the sum of all the odd integers between 0 and 44444? | Answer |
| 3. | Carol has more than one bauble. When she shares them equally between 3 people, there is one bauble left over. When she shares them equally between 4 people, there is still one bauble left over. What is the smallest number of baubles that Carol could have? | Answer |
| 4. | Carol has more than one bauble. When she shares them equally between 2, 3, 4, 5, 6, 7, 8, or 9 people, there is one bauble left over. What is the smallest number of baubles that Carol could have? | Answer |
| 5. | What is the smallest three-digit positive integer whose digits are all non-zero and different? | Answer |
| 6. | How many positive integers are there whose digits are all non-zero and different? | Answer |
| 7. | In a Christmas game, you can win either 4 points or 5 points on your turn, and the game can last any number of turns. What is the largest number of points that it is impossible to end the game on? | Answer |
| 8. | In a different Christmas game, you can win either 495371 points or 2921695 points on your turn, and the game can last any number of turns. What is the largest number of points that it is impossible to end the game on? | Answer |
Red or yellow | ||
| 9. | What is the smallest two-digit positive integer that cannot be written as the sum of consecutive integers? | Answer |
| 10. | What is the smallest four-digit positive integer that can be written as the sum of exactly four consecutive integers? | Answer |
| 11. | Holly drew 18 points on the circumference of a circle then drew straight lines connecting each pair of points. How many straight lines did she draw? | Answer |
| 12. | Holly drew some points on the circumference of a circle then drew straight lines connecting each pair of points. She drew 166047976 straight lines. How many points did she draw? | Answer |
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Comments
Comments in green were written by me. Comments in blue were not written by me.
2026-01-18
Will you be posting solutions? I have what is to me an acceptable answer but I think I might be missing a couple of squaresEwan Leeming
Thanks again for an advent full of brain teasers. Merry Christmas!×2
Gert-Jan
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