Combinatorics
A book has 379 pages. How many 3s in the page number are there.
158
If Bob increases the width of a rectangle by 3 the area will increase by 24, if Bob increases the height of the original rectangle by 7 the area will increase by 84. What is the area of the original rectangle?
96
What is 25^3 - 24^3?
1801
170141183460469231731687303715884105729 is the sum of two primes. What are the two primes? (One Hundred Seventy Undecillion, One Hundred Forty-One Decillion, One Hundred Eighty-Three Nonillion, Four Hundred Sixty Octillion, Four Hundred Sixty-Nine Septillion, Two Hundred Thirty-One Sextillion, Seven Hundred Thirty-One Quintillion, Six Hundred Eighty-Seven Quadrillion, Three Hundred Three Trillion, Seven Hundred Fifteen Billion, Eight Hundred Eighty-Four Million, One Hundred Five Thousand, Seven Hundred Twenty-Nine)
2 and 170141183460469231731687303715884105727
Make 24 with 2, 6, 12, 16
12 + 16 - 6 +2
Nathan has 4 Snickers bars, 2 Kit Kats, and 5 Chocolate coins, how many ways can he arrange them?
6930
How many sides does a Chiliagon have?
1000
1^3+2^3+3^3+4^3+...+9^3 = ?
2025
What is the unit digit of 614^73861? Tip multiply out the number, it only takes like 5 years.
4
Expand (a-x)(b-x)(c-x)(d-x)...(z-x)
0
2*(11C1 + 11C3 + 11C5 + 11C7 + 11C9) = ?
2046
sin(sin(sin(sin(sin(sin(....))))))) <-- Infinite repeating. = ?
0
Find the number of values between 1-1000 that satisfy
x = 4 mod(5)
x = 3 mod(6)
x = 6 mod(7)
5
What is the only number whose english word is in alphabetical order?
forty
5 Girls and 7 Boys are arranged in a circle, how many ways are there to arrange them? Assume every girl is identical and every boy is identical
66
n is a positive integer such that sqrt(sqrt(n^2-63)+18n) is also a positive integer. Find n
12
Find X such that x^13 = 21982145917308330487013369
89
When was 0 invented
3 B.C
A regular tetrahedron (4 sided polyhedron) has vertices (0,0,0) (2,0,0) (1,√3,0), what is the coordinate of the last vertex?
(1, √3/3, (2√6)/3) or (1, √3/3, -(2√6)/3)
Let p and q be prime numbers greater than 3. The number of prime pairs (p,q) for which p^2+5qp+4(q^2) is a perfect square is?
2
24! = 62044cd017332394393ab000
Find the sum of a+b+c+d
18
Which book has an over 360-page proof of 1+1 = 2?
Principia Mathematica by Bertrand Russell and Alfred North Whitehead