Make 24 with 1, 5, 7, 13
Many solutions
ex. (13-7)*(5-1) or (13-1)(7-5)
195 x 205 + 205 x 215
84050
What is the golden ratio in exact form (no decimals)?
(1 + sqrt5) / 2
1.61803...
c2 = a2 +b2 − 2abcosC
Cosine Law
Make 24 using 1, 6, 8, 13
6(13-8-1) = 24!
1 + (2 x 3)4 x 5 / 6
21
What is the only number greater then one that is a perfect square and perfect cube
64
Area = sqrt(s(s-a)(s-b)(s-c))
Heron's formula
Make 24 using 4, 4, 10, 10
(10*10-4) / 4
How many factors does 69420 have?
48
Who was the first person to introduce the concept of calculus?
Newton or Leibniz
(a1 + a2 + ... + an) / n ≥ rootn(a1a2 ... an)
AM-GM Inequality
Make 24 using 1, 3, 9, 10
(1+10)*3 - 9 = 24
1 + 3 + 9 + 27 + ... + 6561
9841
What is Riemann's first name?
Bernhard Riemann
(1 + x)r > rx
r ∈ ℤ, r ≥ 2
x ≥ -1
Bernoulli's Inquality
Make 24 using 1, 3, 4, 6
(6/(1−(3/4)))=24
How many zeroes are at the end of 100!100!100!
72
What score did Evan get on the AMC 10?
69
φ(n)=n[1 - (1/p1)][1 - (1/p2)]...
Where pk is the kth distinct prime factor of n.
Euler Totient Function