Advent calendar 2024
25 December
It's nearly Christmas and something terrible has happened: there's been a major malfunction in multiple machines in Santa's toy factory, and
not enough presents have been made. Santa has a backup warehouse full of wrapped presents that can be used in the case of severe emergency, but the warehouse is locked.
You need to help Santa work out the code to unlock the warehouse so that he can deliver the presents before Christmas is ruined for everyone.
The information needed to work out the code to the warehouse is known by Santa and his three most trusted elves: Santa is remembering a three-digit number,
and each elf is remembering a one-digit and a three-digit number. If Santa and the elves all agree that the emergency warehouse should be opened, they can work out the code for the door as follows:
- Santa tells his three-digit number to the first elf.
- The first elf subtracts her three-digit number then multiplies by her one-digit number. She tells her result to the second elf.
- The second elf subtracts his three-digit number then multiplies by his one-digit number. He tells his result to the third elf.
- The third elf subtracts their three-digit number then multiplies by their one-digit number. Their result is a five-digit number that is the code to unlock the warehouse.
But this year, there is a complication: the three elves are on a diplomatic mission to Mars to visit Martian Santa and cannot be contacted, so you need to piece together their
numbers from the clues they have left behind:
21
138 is an elf's 3-digit number.
11
The third elf's 1-digit number is not 2.
18
The first elf's 1-digit number is not 6.
1
144 is an elf's 3-digit number.
15
The third elf's 1-digit number is not 7.
23
The HCF of the first and third elves' 1-digit numbers is not 1, 2, or 8.
12
The second elf's 1-digit number is not 2, 8, or 1.
8
The third elf's 1-digit number is not a factor of 575.
17
The first elf's 1-digit number is not 9.
20
The third elf's 1-digit number is not 4.
7
The third elf's 1-digit number is not 1.
4
The third elf's 1-digit number is not 9.
6
990 is a multiple of an elf's 3-digit number.
3
The first elf's 1-digit number is not 7.
22
The HCF of 851 and the third elf's 3-digit number is 1.
14
The second elf's 1-digit number is not 6, 2, or 5.
24
Santa's number is 444.
9
The first elf's 1-digit number is not 5.
5
The second elf's 1-digit number is not 1, 7, or 9.
10
The second elf's 1-digit number is not 4, 9, or 5.
13
One of the digits of the second elf's 3-digit number is 9.
19
The HCF of 256 and the second elf's 3-digit number is 1.
2
The first elf's 1-digit number is not a factor of 202.
16
The first elf's 1-digit number is not 3.
21
138 is an elf's 3-digit number.
11
The third elf's 1-digit number is not 2.
18
The first elf's 1-digit number is not 6.
1
144 is an elf's 3-digit number.
15
The third elf's 1-digit number is not 7.
23
The HCF of the first and third elves' 1-digit numbers is not 1, 2, or 8.
12
The second elf's 1-digit number is not 2, 8, or 1.
8
The third elf's 1-digit number is not a factor of 575.
17
The first elf's 1-digit number is not 9.
20
The third elf's 1-digit number is not 4.
7
The third elf's 1-digit number is not 1.
4
The third elf's 1-digit number is not 9.
6
990 is a multiple of an elf's 3-digit number.
3
The first elf's 1-digit number is not 7.
22
The HCF of 851 and the third elf's 3-digit number is 1.
14
The second elf's 1-digit number is not 6, 2, or 5.
24
Santa's number is 444.
9
The first elf's 1-digit number is not 5.
5
The second elf's 1-digit number is not 1, 7, or 9.
10
The second elf's 1-digit number is not 4, 9, or 5.
13
One of the digits of the second elf's 3-digit number is 9.
19
The HCF of 256 and the second elf's 3-digit number is 1.
2
The first elf's 1-digit number is not a factor of 202.
16
The first elf's 1-digit number is not 3.
You can to open the door here.