Problem 61: Triangle and Circles

Rich Tasks 16: Square Challenge

Rich Tasks 15: For the Love of Logarithms

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from https://integralmaths.org/samples/Problem_solving_shorts%20_samples.pdf

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Resource: https://undergroundmathematics.org/exp-and-log/summing-to-one

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Problem 60: How many cats?

 

Recently I came across this tweet. This work belongs to Italian illustrator and artist Franco Matticchio. Good for my archive.

As anyone feels when seeing this work, I also started counting the number of cats in this illustration. How about you?

How many cats are in this drawing by Italian artist Franco Matticchio? https://t.co/7zm23qdBoo pic.twitter.com/Vdj1TbshRc

— Cliff Pickover (@pickover) July 4, 2018

Rich Tasks 14: Mondrian Puzzles

Piet Mondrian is a Dutch artist famous for his artworks made of rectangles.

Here is a challenge:

-Take a square canvas, say 4x4, 5x5, 6x,6 or 8x8. 
-Divide it into rectangles.
-The canvas must be entirely covered by non-overlapping rectangles.
-All side lengths must be whole numbers.
-No two rectangles can have the same dimensions. (You cannot have a 3x2 and a 2x3 rectangle together)
-What is the minimum difference between the area of the largest rectangle and the smallest?

Example: 7x7 canvas, lowest score is 8-3=5

Your Turn

Moderated from TedEd and Numberphile

Rich Tasks 13: Sagrada Familia "Magic" Square

The Temple Expiatori de la Sagrada Familia is a Roman Catholic Church which is under construction since 1882. 

In front of the unfinished building, there appears a "magic" square as shown. 

Designed by the sculptor Subirach, any sequential four numbers (same row, column, diagonal or other ways) on the magic square add up to 33, in 33 different ways. 

Actually, this is German mathematician Durer's famous 34 square changed by the sculptor in order to reach Jesus' age when he died. Normally there should be numbers from 1 to 16 without repetition. 

Can you show all the patterns giving 33 on the given magic squares below? First two are given as the example. 

Resources:

1.@robeastaway

2.http://www.taliscope.com/Sagrada_en.html

Problem 59: The Stone on the Grave of Diophantus

The gods granted him childhood for a sixth of his life, and a twelfth for his adolescence. A barren marriage took up a seventh of his life. Five years passed, and then a child was born to him. No sooner had this child reached half the age of its father than it died. Diophantus lived for four more years, drowning his pain in the study of numbers, and then gave up his life.

Resource

Problem 58: Factorial Frenzy

(moderated from @Feynmaths)

Problem 57: Reflection

Problem 56: Highest 5-digit number

by Kumi Yamashita

Using the numbers 1 to 9 one time only, a 3-digit number and a 2-digit number will be generated. Then these two numbers will be multiplied. What is highest possible product?

Problem 55: Fill in the table

Which of the following is most suitable to write instead of the question marks?

Problem 54: Isosceles Triangles

This is an isosceles triangle. Two of its sides are equal in length to each other.

How many such triangles exist given that their perimeter is 100 and all side lengths are whole numbers?

1. 24
2. 25
3. 49
4. 50
5. none

Problem 53: Number Puzzle

Retweet if you can solve the answer! pic.twitter.com/1KshVfM2x0

— Drew@Maths (@drewfoster0) June 11, 2018

Problem 52: Iceland's World Cup Adventure

http://www.goal.com/en-gb/news/russia-2018-iceland-becomes-smallest-nation-to-qualify-for-world-/1gwdmlxhdwsui1hzp4o0nu6rgz

Iceland participates to the Soccer World Cup for the first time in history. The people of this small island nation so excited.

They are going to play with Costa Rica, Argentina and Nigeria in the group stage.

Can you determine in how many different ways can they qualify to the second stage? This includes being in the top two positions. Points may vary for qualifying to the upper level. For example, consider all the games are draw. Then all teams will have 3 points each. Some other rules will be used to determine the teams which qualify.

Here are some other examples:

1. Argentina 9 points

2. Iceland 6 points

3. Nigeria 3 points

4. Costa Rica 0 points

1. Iceland 9 points

2. Costa Rica 7 points

3. Argentina 4 points

4. Nigeria 0 points

Problem 51: Missing Numbers

In this easy puzzle, you should discover the pattern and find the missing numbers.

Rich Tasks 12: Brand Logo Activity (Transformations)

You are a project designer. Your job is to analyze different logos and determine what type of transformations they used. Your assistant provided you the following table. Fill in the following table and explain the transformations.

Logo	Transformation	Description

Download the pdf

Problem 50: Number Challenge

In this number challenge you are going to start with a three digit number. Next step, you should write one less of the first number to the end and double the second and third digit and write the result to the front in the new number.

Here is an example:

1.      812

2.    247

3.     941

4.   827

5.     547

6.   946

7.    928

8.   568

9.    1364

In this example, the numbers reach to four digits in nine steps. It is not possible to reach to the ninth step every time as you can see below:

1. 124

2.480

3.1603 

Can you produce sequences of numbers continuing with more than nine numbers?

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