Maths Club Week 3

Adding in Zn

100

In Z₅, what is 4+3?

2

200

In Z₂₃, what is 19 + 20?

16

Gauss is my favourite mathematician

100

What is the sum of the first 20 positive integers?

210

200

There are 15 people in a meeting. Everyone shook hands with everyone. How many hand shakes were there in total?

105 handshakes.

300

What is 5+6+...+24+25?

315

400

In a chess board, I put a $100 coin in the first square. Then, on the second square, I put 2 $100 coins. On the third square, I place 3 $100 coins. I continue in the same way, always putting in each square a pile of coins with one more coin than the pile on the previous square. How much money is on the board?

$208,000

500

On the first of February 2025, Charles had 5 $100 coins in his piggy bank. On Feb 2nd, he put 7 $100 coins in the piggy bank. The next day, he added 9 more $100 coins. Each day, the number of coins he added was two more than the number of coins he added the previous day.

How much money did he have at the end of February?

$82,600

Multiplying in Zn

100

In Z₁₁, what is 9(8)?

6

200

In Z₁₂, we have that any number times zero equals zero. Are there any other pairs of numbers that multiplied together give us zero? If so, write all of them.

Yes. 2x6 and 3x4, 6x4, 8x3, 6x6, 9x4

300

We know that in the rational numbers, the equation

5x = 1

has solution x = 1/5. What is the solution to the same equation in Z₇?

x = 3

400

Find all solutions to the equation 3x = 6 in Z₁₂

{2, 6, 10}