Algebra
Number Theory
Combinatorics
Festive Teatime
100
What is the largest n such that 10^n divides:
2024!
503
100
What is the largest number x such that the numbers
x, x-2, x-4
are all prime? (or do infinite such x exist?)
x=7
100
Santa gives out a 10 question T/F test to determine if a child is naughty or nice. If is guaranteed a score of at least 4 if they guess 5 T's and 5 F's, how many possible answer keys could Santa have?
What is 22?
100
Budget Chaos Wheel: Pick two teams and swap their points.
:3
200
What is the sum of all nonnegative integers n such that n^2+1 divides n+1 perfectly?
1
200
At midnight on December 25th (604800 seconds before New Years), Basil begins counting down to New Years (in seconds) and they do not stop until they reach 0. However, Basil does not like palindromic numbers, and so they skip them when counting. Basil incorrectly assumes that counting to -2024 instead of counting to 0 will fix this error. By how many seconds will Basil be off, and in which direction?
Basil will be 422 seconds too late.
200
Santa is arranging a secret Santa with 6 of his reindeer. The reindeer each pull a random name out of a hat. What is the probability the reindeer all pull someone else's name?
What is 53/144?
200
Quick, is the number 221 prime?
No, it divides 17 and 13.
300
Determine:
(2+3)(2^2+3^2)(2^4+3^4)...(2^1024+3^1024)
3^2048-2^2048
300
Order the numbers from 2 to 12 such that for any number N that comes after any number M in this permutation, there exists a number with M factors that is less in value than any number with N factors.
2, 3, 4, 6, 8, 5, 9, 10, 12, 7, 11
As 2 has 2 factors, 4 has 3 factors, 6 has 4 factors, 12 has 6 factors, 24 has 8 factors, 32 has 5 factors, 36 has 9 factors, 48 has 10 factors, 72 has 12 factors, 128 has 7 factors, and 2048 has 11 factors.
300
Santa has 5 elves, 4 children and 7 reindeer. He is arranging a Christmas dance and wants to ensure everybody is assigned to a partner of a different species. Find the number of ways to do this. (Assume everybody is unique and thus distinguishable)
What is 100800?
300
In what country was eggnog invented?
Britain
400
How many solutions does the equation 
have in the closed interval 
?
2
400
A Hanukkah candle holder holds a maximum of 9 candles in 9 separate positions. Celeste owns some number of Hanukkah candle holders. Celeste observes that when they write out the number of ways they can place exactly one candle on each candle holder they own, the last two digits form a prime number. If the number of candle holders Celeste owns exceeds 6, what is the smallest number of candle holders they could own?
9
400
Rudolph is looking for matching socks. He looks in his closet, where there are 100 sets of 4 matching socks. If he still hasn't got a matching quadruplet after 199 socks pulled, find the probability he does after 200 socks.
What is 99/101?
400
Unlike the Western New Years, Chinese New Years occurs on a different day in the Western Calander every year. What day does it occur on next year?
January 29th
500
Santa has made a new machine. There are two distinct input sections (1 and 2), and one output section. Santa observes that placing the same amount of coal (in kilograms) in both sections always outputs one kilogram of coal. Furthermore, Santa observes that given any three positive numbers A, B, and C, placing B kg of coal in slot 1 and C kg of coal in slot 2, and then taking the result and placing it in slot 2, and finally placing A kg of coal into slot 1, returns the same amount of coal as placing A kg of coal into slot 1 and B kg of coal into slot 2 C times. What happens when Santa places 10kg of coal into slot 1 and 100 kg of coal into slot 2?
Outputs 0.1kg of coal
500
How many digits are in the decimal representation of 2024! ? (Award to closest team. x2 points if they get the exact number)
5815
500
Santa has ordered a new sleigh for $2010. He only has 2, 5 and 10 dollar bills. How many ways can he pay?
What is 20503?
500
Budget chaos wheel: Pick a team to lose 500 points :3
:3