What is the net of an oblique cylinder, and what is its surface area?

# 100!

# The Numbers’ Dress-up Party

https://twitter.com/DavidKButlerUoA/status/895910228058710016 All the numbers have come to a dress-up party in full costume. They all know themselves which costume everyone else is wearing, but you don't know. If you pick any two of them and ask them to combine with +, -, ×, or ÷, they will point out which costume is the correct answer, … Continue reading The Numbers’ Dress-up Party

# Book-ended Sixes

Find the smallest number n, such that n ends in a 6, and when n is multiplied by 4 it makes a number that is n with the 6 in the front.

# Making Forty

Use all of these symbols and only these symbols to produce the number 40: (())xxx+++3331111 **Extension** - What is the largest number that can be made using all those symbols? - What is the smallest number that can be made using all those symbols? - What is the smallest odd number that can be made with those symbols?

# Hexagon in a Circle

Hexagon with verticies on a circle has three consecutive sides 3 and three consecutive sides 5. What is the area of the circle?

# Consecutive Integers

Three consecutive integers are multiplied together, and the middle number is added to the total. E.g. $latex (4 \times 5 \times 6)+5=125=5^3$ Prove that this is always true, with any set of three consecutive integers.

# Function Fun

Suppose $latex f(3) = \sqrt(3)$ $latex f(-a) = -f(a)$ $latex f(a+b) = \frac{f(a)+f(b)}{(1-f(a)f(b))}$ Evaluate $latex f(1)f(2)f(3)f(4) $

# n to the Five

Is $latex n^5 + 5^n $ ever prime?

# Angles on a Grid

$latex x+y+z=? $ Note: The big square is divided into nine small squares of equal size.

# Puzzlebomb 55

Fill the grid with the numbers 1-35, using the clues given, so that each row contains 7 numbers each with a different remainder when you divide by 7, and each column contains 5 numbers each with a different remainder when you divide by 5. The numbers in each of the dotted regions add up to … Continue reading Puzzlebomb 55