Alg
Geo
Combo Wombo
Number Theory
Cook or be Cooked
100
Find the sum of the numbers: 2 + 5 + 8 + ... + 98 + 101
1751, Note that the numbers increase by 3, so 2 + 3k = 101, so
k = 33. Therefore, there are 34 numbers.
We divide into pairs (2 + 101) + (5 + 98) + ⋯ = 17 ∙ 103 = 1751
100
Place four ones, four twos and three threes in a circle so that the sum of any three consecutive numbers is not divisible by 3
1-1-2-1-2-2-2-3-3-1-3.
Cyclic permutations and reverse permutations are also an option.
100
Mr. Wolf has beat Mr. Bangs in baseball and now will get a fried chicken sandwhich!! For Mr. Wolf choices he has 4 different types of vegetables and 5 different types of sauce he can add to his sandwhich? Assuming he can only put on 1 vegetable and 1 sauce in the sandwich, how many combinations does Mr. Wolf have?
20
100
Bruno wants to hide the Math Team budget in a secure safe with a 4-digit password. In secret, Daniel learns from Bruno that the password is the largest 4-digit number that is divisible by 7 and can be written in 4 different digits. What is the password?
9870, (since 987 is biggest 3 digit number divisible by 7 that doesn't have same digits in it)
100
What do mathematicians always forget to write in their answer to a question about integration?
+C
200
In 2050, The elevator in the 20-story school called Hcet Nylkoorb is broken: it can either go up 8 floors or go down 13 floors. Is it possible to get from the 20th floor to the first floor using the elevator? (please say in how many attemps you can get there OR why you can't there)
No - There is only one way to go: 20-7-15-2-10-18-5-13, but you can’t leave from the 13th floor
200
What is the minimum number of queens that can be placed on a 5x5 checkered board so that all the squares are under attack? (A queen is a piece that can attack any number of squares vertically, horizontally, or diagonally and in any direction)
3 queens;
OOOXO
OOOOX
OOXOO
OOOOO
OOOOO
200
Isfar bought 5 energy drinks for the next academic week. 3 of them are strawberry flavored, 1 is orange flavored, 1 is "classic" flavored. In how many ways can Isfar drink all these energy drinks?
5! : 3! = 20
200
What is the ending digit of the difference
1 · 2 · 3 · 4 · … · 2021 − 1 · 3 · 5 · … · 2019 · 2021?
5 - first number will have end digit of 0 because 2 * 5 = 10 and second number will have end digit of 5 because it's divisible by 5 and odd. 10 - 5 = 5
200
Where can you find somewhere saying: Two twos croski
Toronto
300
The fraction 32/49 is written on the board. In one action, Martin can either add 1 to the denominator, or subtract 1 from the numerator, or reduce the fraction, or multiply the numerator and denominator by the same number. After what minimum number of actions can he obtain the fraction 2/3?
never - 32/49 < 2/3, all those actons are decreasing/keeping the same original fraction.
300
The clock shows 9:15. What is the angle between the minute and hour hands?
172.5 degrees (180 - 7.5 = 172.5) (7.5 is dispalcement of of hour hand from 9)
300
How many permutations are there of the word ”BROOKLYNLATIN”? (consider it as singular word (you can use calculator for this one))
778 377 600 = 13! / 2 / 2 / 2
300
Write the first eight prime numbers in a row and cross out 6 digits so that the resulting number is the largest.
8 prime numbers = 235711131719, cross out = [235]7[111]31719, get = 731719
300
Which basketball player is the best at math?
Jaylen Brown
400
Ishowspeed runs at a constant rate and stops for a five-minute break at the end of every mile. Kipchoge runs at a constant rate which is three-quarters the rate that Speed runs , but Kipchoge takes a five-minute break at the end of every two miles. Kipchoge and Speed begin running at the same time and arrive at the 50-mile mark at exactly the same time. How many minutes has it taken them?
620
400
In parallelogram ABCD the bisectors of angles A and D intersect at the midpoint of side BC.
Find AD if AB = 5.
10; ∠BEA = ∠EAD, since BC ∥ AD, then ABE is isosceles, so AB = BE. Therefore,
AD = BC = 2AB = 10
400
Adir says that if the next week he will have 2 or more big tests in one day when he is cooked. What is the chance that he is cooked if there are 3 tests next week?
(5^3 - 5 * 4 * 3)/ 125 = 65/125
400
In order to get pocket money from his parents, Nikita needs to find the number of positive integer pair solutions to the equation:
(1+2a)(2+2b)(2a+b)=32ab
None lol
400
Who invented the law of cosines?
Jamshīd al-Kāshī (persian mathematician)
500
Mr. G-K forgot the code from his locker with calculators. The code for the locker is a two-digit number. Mr. G-K forgot the code, but he remembers that the sum of the digits of this number, added to their product, is equal to the number itself. Write all possible versions of the code so that Mr. G-K can open the locker faster.
19, 29, 39, 49, 59, 69, 79, 89, 99
(x + y) + x · y = 10x + y
x · y = 9x
y = 9 and x is any other digit except 0
500
(Arihunt will make diagram for this one) Nolan and Madison Beer hop on a gondola, N in a Disney World ferris wheel. Nolan says "Fist Bump!" as they are at the highest point in the ferris wheel. Directly below gondola N is Chandler riding on gondola C. All 16 of the gondolas on the ferris wheel are each connected by a thin wire going towards the center of the Mickey Mouse, M. Find the angle measurement of NMC.
180 degrees. Did yall think it was 22.5 hahaha
500
Let's put the fries in the bag. There are two types of fries: salted and unsalted. If it takes 3 workers, 2 hours to make 16 salted fries and 50 unsalted fries. How many unsalted fries can 5 workers make in 3 hours? (Assume all workers work the same and the ratio of the fries is always constant.)
125
500
Mr. Baker, a mathematician, wrote the following numerical puzzle on the board:
+ =
(three-digit natural number + four-digit natural number = five-digit natural number). Bogdan, a student, said: "It's easy." And Mr. Baker added: "If you read these numbers in reverse order (turn each number upside down), you will also get a correct equation." Help Bogdan find all such numbers.
222 + 9779 = 10001; 212 + 9889 = 10101; 202 + 9999 = 10201
Adding a three-digit and a four-digit number, we get a five-digit number in this puzzle. So, the extreme digits of the result are ones, the extreme digits of the four-digit number are nines, the extreme digits of the three-digit number are twos. We get: 2*2+9**9=1***1. Going through the options, we get three solutions
500
Why did 7 eat 9?
To get 3^2 meals a day