Rich Tasks 57: Four Twos

Rich Tasks 56: Powers 2

Also look: Different forms of a number
                  Powers 1

Rich Tasks 55: Powers 1

Also look: Different forms of a number

Rich Tasks 54: Visualizing Multiples of 45

• Write the first 20 multiples of 45.
• Do you see any patterns? Is there a shorter way to find them all?
• Place the last two digits numbers you found around the icosagon (20-sided polygon)
• Join the points in order of appearance.
• What visualization do you get, when you do the same process with 55?
• Do the same procedure with 35, 25 and 15.
• How about the multiples of 3? What polygon should you use?

Problem 116: The Mistery Multiplication

Find all the unknown numbers shown with dots.

source

Rich Tasks 53: Comparing Brand Values

Use a spreadsheet and display this infographic with a suitable chart.

Source: https://www.visualcapitalist.com/the-worlds-100-most-valuable-brands-in-2019/

Problem 115: Math Question From 'Little Man Tate'

How about giving me a number that when divided by the product of its digits the quotient is 3, and if you were to add 18 to this number the digits would be inverted?

Beautiful Gifs 9: The Sieve of Eratosthenes

Source https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

Problem 114: Factorial Sequence

Rich Tasks 52: Factorials Exercises

Rich Tasks 51: 'What is your magic number?' (Birthday Magic Square)

With any given top row, we can complete a fourth-order magic square. 

Part 1

Here is a magic square made by the birthday of the famous mathematician Ramanujan. (22 December 1887)

In this magic square rows, columns and diagonals add up to 139. 

However, there are so many other patterns in this magic square. How many can you find?

Part 2

What is your magic number? Can you complete a magic square with the date of your birthday in the top row?

Write your birthday on the top row following the instructions below:

(i) Place the special date in the first row

(ii) b+c = m+p [there are many different possible values]

(iii) a+p = g+j [there are many different possible values]

(iv) m+d = f+k [there are many different possible values]

(v) b+n = g+k

(vi) c+o = f+j

(vii) a+m = h+l [there are many different possible values]

(viii) All rows, columns and diagonals must add up to the same total

Sources
- https://apfstatic.s3.ap-south-1.amazonaws.com/s3fs-public/ramanujans_honour_magic_square.pdf
- https://nrich.maths.org/1380
- https://en.wikipedia.org/wiki/File:Magic_Square_Ramanujan.svg

Problem 113: Sums of Odd Numbers

Use the above figure only to find

1+3+5+7+....+49=?

Inspired by @Mathgarden

Rich Tasks 50: Twelve Envelopes Puzzle

source: @mathequalslove

Math Pics 14: Correlation vs Causation

Source

Problem 112: Sierpinski Triangles

What is the ratio of the black coloured triangles to the full triangle in the fourth iteration of the Sierpinski triangles?

Problem 111: Shaded Area

Imagine this pattern of triangles inside the big triangle goes infinity.

What is the ratio of the red area to the triangle's area?

(Source)

Problem 110: Fathers and Sons

My father is 4 times as old as I am.

5 years from now, he will be 3 times as old as my age.

15 years later, he will be 2 times as old as I will be.

How many years ago, was his age 6 times as old as I was?