Problem 68: Toppled Square

What is the area of the toppled square?

Resource: @Cshearer41

What’s the area of the toppled square? pic.twitter.com/77yHacED5Y

— Catriona Shearer (@Cshearer41) August 7, 2018

Problem 67: Digital Clock

This is a fun problem! #iteachmath #PCTM2018 pic.twitter.com/0DRCg3xnwR

— Stephanie Diehl (@MathDiehls) August 6, 2018

-How many times in a 12-hour period will the digits on a digital clock have a sum of 10?


-How many times will they add up to 13?

Rich Tasks 18: Triangle of Power

Inspired by 3Blue1Brown

Rich Tasks 17: Square Number Challenge

one solution:

Problem 66: Soccer and Pythagoras

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Problem 65: Rectangular Prism with Same Volume and Surface Area

Can you construct a rectangular prism such that its volume and surface area will have same numerical value?

Problem 64: Rolling Rectangle

This question is moderated from Brilliant.org's Weekly quiz for this week. The original question can be reached from this link.

Beautiful Gifs 6

via GIPHY

via GIPHY

Problem 63: Pattern

Problem 62: Lowest Common Multiple

The sum of four different positive integers is 100. What is the smallest value of the LOWEST COMMON FACTOR of these four integers?

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What is the answer if the sum is 500?

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What is the answer if the sum is 600?

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What do you notice?

This question is taken and adapted from Brilliant.org.

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