AoPS: Resigned Resolutions

Since I always fail my New Year's resolutions, this year, my New Year's resolutions are:

1. Make a new year's resolution
2. Fail my new year's resolution

Am I guaranteed to succeed? Guaranteed to fail? Something else?

AoPS: Weird Equation

Let weird(n) be the number of ways to write n as a + a + b + c, where n, a, b, and c are distinct positive integers. Is weird(n) an increasing function?

Year 8 Maths Homework: Find The Radius

Could you solve this? My year 8 daughter’s homework from last weekend. I did point her in the right direction and then she finished it off. She was very happy as she worked out how to solve it.

Last night, she asked if she could work on really hard maths over half term, to help her find maths at school easy and also to have fun (apparently). I’ve pulled out UKMT’s Intermediate Problems by Andrew Jobbings (years 9-11 Intermediate Maths Challenge questions) and a pile of Art of Problem Solving books.

AoPS: Sum 25 Product

A set of positive integers has sum 25. What is the biggest you can make the product of the numbers?

Outwood Academy Valley: Area of the Square

Can you work out the area of the inner square?

Parallel (Simon Singh): Intermediate Maths Challenge - Patterns

The pattern 123451234512345... is continued to form a 2000-digit number. What is the sum of all 2000 digits?

6000
7500
30,000
60,000
75,000

UKMT (UK Mathematics Trust): [√ n]

The notation [√ n] means the integer part of the square root of n. How quickly can you solve?

Outwood Academy Valley: Matchstick Puzzle

Take away two matches to leave two squares.

Parallel (Simon Singh): Musical Mathematics

It is extraordinary that so much of the universe can be explained using mathematical equations. Indeed, it is often said that mathematics is the language of the universe. It is certainly the language of science.

In this clip, from a documentary in the American Nova series, the jazz musician Esperanza Spalding explains how maths is also at the heart of music. Pay attention to the way that numbers relate to musical intervals (an octave, a fifth and a fourth).

AoPS: The Four Cards

Shawn has dealt four cards in front of you. He claims that if a card has an even number on one side of it, then the other side of the card is blue. Which cards do you need to turn over, in order to confirm if Shawn is telling you the truth?

NRICH: Shear Magic

Shearing is a transformation of a shape in which a particular line (in this case the base of the triangle or parallelogram) remains fixed and all other points in the shape are translated parallel to that line by an amount proportional to the distance from that line.

Maths Challenge: What is height of full iceberg?

A cone shaped iceberg with tip pointing up is 80% submerged in water. Part I can see is 8m high & 6m across. What is height of full iceberg?

Outwood Academy Valley: Polyominoes

2. Is there a link between the number of squares in a polynomial (a shape made out of squares joining on a complete edge) and the minimum perimeter that can be made for each number of squares?

Parallel (Simon Singh): The Rhind Papyrus

The Ancient Egyptian Rhind Papyrus dates back to around 1550 BC and is full of mathematical ideas and puzzles. Not surprisingly, it has a section about calculating the slopes of pyramids.

I particularly like that it opens with the statement: “Directions for Attaining the Knowledge of All Dark Things”. That’s quite a way to describe mathematics.

The papyrus has a great deal about “Egyptian fractions”, which means that every fraction has to be described in terms of other fractions which have the numerator 1.

UKMT: Vertices of a Cube

Can you solve?

Parallel (Simon Singh): Googol

The mathematical term “googol” was invented in 1920 by 9-year-old Milton Sirotta, nephew of American mathematician Edward Kasner. A googol is 10100, which means it is written as 1 followed by one hundred zeroes.

The fact that it can be written in such a compact form, 10100, is deceiving, because it represents a phenomenonally gigantic number of mind-blowing proportions. A googol is about one hundred billion billion times bigger than the number of particles in the visible universe (1080).

Although the company and search engine Google is spelt differently, it based its name on the huge number googol, because its ambition was to provide users with huge amounts of information.

What is googol squared?
What is √(googol)?

Art of Problem Solving (AoPS): True or False

Each statement is either true or false. How many of the following statements are true?

1. The answers to statements 2 and 3 are different.

2. The answers to statements 3 and 4 are different.

3. The answers to statements 4 and 5 are different.

4. The answers to statements 5 and 6 are different.

5. The answers to statements 6 and 7 are different.

6. The answers to statements 7 and 8 are different.

7. The answers to statements 8 and 1 are the same.

8. The answers to statements 1 and 2 are the same.

UKMT: Who is Telling the Truth & Who is Lying?

Hands up!

How good are you at working out his style of maths word problem?

Number Search (Simon Gregg)

If the smallest equilateral triangle (light green) is 1, what other numbers can you see?

AoPS: Don't Flip Out

Alex has 25 discs that are black on one side and white on the other. He arranges them on a 5 x 5 grid so that all the white sides are showing.

A move consists of taking any three consecutive discs in a row or column and flipping them over. You want the discs to make the checkerboard coloring shown below.

From the initial all-white position, what is the smallest number of moves needed to get to the checkerboard position?

LANDO EDucation

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