Musa's Birthday Math Jeopardy - Advanced

Counting

200

What is the next number?

1, 2, 3, 4, ...

5

400

What is the next number?

12, 13, 14, 15, ...

16

600

Counting backwards what is the next number?

11, 10, 9, 8, ...

7

800

Counting by twos what is the next number?

2, 4, 6, 8, 10, ...

12

1000

How many pairs (sets of two) can be made from a set of four things?

six

Powers of Numbers

200

0⁵

0

400

1⁸

1

600

2³

8

800

3⁶

729

1000

2¹⁴

16,384

Prime Factorization

200

Give the prime factorization of 6.

2 * 3

400

Give the prime factorization of 77.

7*11

600

Give the prime factorization of 162.

2*3⁴

800

Give the prime factorization of 216,000,000.

2⁹*3³*5⁶

1000

Give the prime factorization of 5040.

2⁴*3²*5*7

Modular Arithmetic

200

3 + 5 (mod 7)

1

400

8 * 3 (mod 5)

4

600

Solve for x:

6 * x = 1 (mod 17)

x = 3

800

Solve for x:

5*x = 1 (mod 11)

x = 9

1000

3^1001 (mod 13)

9

Infinite Series

200

1 + 1/2 + 1/4 + 1/8 + 1/16 + ...

2

400

1 + 2/3 + 4/9 + 8/27 + 16/81 + ...

3

600

1 + 1/4 + 1/9 + 1/16 + 1/25 + ...

π²/6

800

1 + 1/16 + 1/81 + 1/256 + 1/625 + ...

π⁴/90

1000

While 1 + 2 + 3 + 4 + 5 + ... diverges, using Zeta function regularization it can be assigned what value?

-1/12