Puzzles
25 December
It's nearly Christmas and something terrible has happened: after years of gradual wear and tear, Santa's magic sleigh has fallen apart.
You need to help Santa build a new sleigh so that he can deliver presents before Christmas is ruined for everyone.
The magic sleigh was built from parts bought from magic factories all over the world, and only the exact combination of parts will be magic enough to let Santa deliver all
the world's presents on Christmas Eve—but it's been a long time since a magic sleigh was last built and no-one can remember exactly which combination of parts is needed.
You need to use the clues below to work out which parts to order to build a new magic sleigh. There are five parts that you need to order
(runners, a chassis, a present holder, a seat for Santa, and a front of the sleigh with reins). There are nine suppliers (numbered from 1 to 9) that Santa can order parts from.
10
The chassis should not be ordered from 918
The chassis should not be ordered from 712
One of the parts should be ordered from 28
The chassis should not be ordered from 49
The front should not be ordered from 51
The chassis should not be ordered from 67
Santa's seat should be ordered from 3, 5, or 46
The front should not be ordered from 814
One of the parts should be ordered from 413
The runners should not be ordered from a factor of 17520
Today's clue and the clue on 19 December are false4
The chassis should not be ordered from 52
The chassis should not be ordered from 15
The chassis should not be ordered from 324
Santa's seat should be ordered from 6, 7, or 517
The runners should be ordered from 511
The chassis should not be ordered from 421
One of the parts should be ordered from 83
The front should not be ordered from 119
Exactly 4 of the clues are false15
The chassis should not be ordered from 1, 2, or 823
The chassis should be ordered from 422
The chassis should be ordered from 416
One of the parts should be ordered from 110
The chassis should not be ordered from 918
The chassis should not be ordered from 712
One of the parts should be ordered from 28
The chassis should not be ordered from 49
The front should not be ordered from 51
The chassis should not be ordered from 67
Santa's seat should be ordered from 3, 5, or 46
The front should not be ordered from 814
One of the parts should be ordered from 413
The runners should not be ordered from a factor of 17520
Today's clue and the clue on 19 December are false4
The chassis should not be ordered from 52
The chassis should not be ordered from 15
The chassis should not be ordered from 324
Santa's seat should be ordered from 6, 7, or 517
The runners should be ordered from 511
The chassis should not be ordered from 421
One of the parts should be ordered from 83
The front should not be ordered from 119
Exactly 4 of the clues are false15
The chassis should not be ordered from 1, 2, or 823
The chassis should be ordered from 422
The chassis should be ordered from 416
One of the parts should be ordered from 1You can use this page to try ordering parts for a sleigh.
24 December
3 and 5 are both factors of 2025, and 3 and 5 are the only two prime numbers that are factors of 2025.
What is the largest three-digit number that has both 3 and 5 as factors and no other prime numbers as factors?
23 December
153 is equal to the sum of the cubes of its digits: 13 + 53 + 33.
There are three other three-digit numbers that are equal to the sum of the cubes of their digits. What is the largest of these numbers?
22 December
Put the digits 1 to 9 (using each digit exactly once) in the boxes so that the sums are correct. The sums should be read left to right and top to bottom ignoring the usual order of operations. For example, 4+3×2 is 14, not 10.
Today's number is the product of the numbers in the red boxes.
| × | + | = 11 | |||
| × | ÷ | + | |||
| ÷ | ÷ | = 1 | |||
| – | – | ÷ | |||
| + | – | = 1 | |||
| = 1 | = 0 | = 1 |
21 December
There are ten ways to make a list of four As and Bs that don't contain an even* number of consecutive As:
|
|
How many ways are there to make a list of eleven As and Bs that don't contain an even number of consecutive As?
* We don't count 0 consecutive As as being an even number of consecutive As.
20 December
A number is called a perfect power if it is equal to nk for some integer n and some integer k > 1. 2025 is a perfect power (452)
and 23 more than 2025 is also a perfect power (211).
What is the only three-digit perfect power that is 29 less than another perfect power?
19 December
Eve uses the digits 1, 2, 3, 4, 5, 6, 7, 8 and 9 to write five square numbers (using each digit exactly once). What is largest square number that she made?
18 December
There are 5 different ways to make a set of numbers between 1 and 5 such that the smallest number in the set is equal to the number of numbers in the set. These 5 sets are: {1}, {2, 3}, {2, 4}, {2, 5} and {3, 4, 5}.
How many ways are there to make a set of numbers between 1 and 14 such that the smallest number in the set is equal to the number of numbers in the set?