This is a lovely result from Futility Closet.
“Draw an arbitrary quadrilateral and divide each of its sides into three equal parts. Draw a line through adjacent points of trisection on either side of each vertex and you’ll have a parallelogram.
Discovered by Austrian engineer Ferdinand Wittenbauer.”
Find a proof.
See Wittenbauer’s Parallelogram for a solution.
This puzzle, from another set of seven challenges assembled by Presh Talwalkar, turned out to be very challenging for me.
“This is a fun problem I saw on Reddit AskMath. A circle contains two squares with sides of 4 and 2 cm that overlap at one point, as shown. What is the area of the circle?”
This took me quite a while to figure out, but I relied on another problem I had posted earlier.
See Two Squares in a Circle for solutions.
Here is a probability problem from BL’s Weekly Math Games. Normally I am not a fan of such problems, but this one seemed fairly straight-forward for a change.
“I hit the target 75% of the time. You hit the target 25% of the time. We aim at the same time, and only one bullet hits. What’s the probability it came from me?
Now as for this puzzle, it would be tempting to think that I am 3 times as good at hitting the target, but I am not!”
See Whose Bullet for a solution
This is another problem from A+Click.
“As each of five eggs is weighed, the average weight increases by one gram each time. If the first egg weighs 50 grams, what is the weight of the last egg?
Answer Choices: 55 grams 56 grams 57 grams 58 grams”
See Weighing Eggs for solutions.
I thought this puzzle, which was included among a set of seven challenges assembled by Presh Talwalkar, would be fairly straight-forward.
“A cube of 50 cm is filled halfway with water. A rectangular prism with a square base of 25 cm and a height around 50 cm is placed flat onto the base of the cube, as shown. By how much does the water level rise?
Thanks to Fahad Alomaim for the suggestion! This is translated from a Mawhiba curriculum question for 8th grade.”
But I got the wrong answer and found Talwalkar’s solution a bit hard to fathom at first. Looks like I flunked 8th grade.
See Brick in Water Puzzle for solutions.
This is another challenging sum from the 2024 Math Calendar.
“Find x where x = et and
”
As before, recall that all the answers are integer days of the month.
See Yet Another Sum for a solution.
Continuing the logic thread, this is a nice logic problem from MathsJam Shout for April 2025.
“The king of the spiders has four servants, and the servants have either 6, 7, or 8 legs. Servants with 7 legs always lie, and servants with 6 or 8 legs always tell the truth.
The king asks ‘How many legs do you four have in total?’, and the four spider servants (who are standing behind a table, so you can’t see their legs) answer 25, 26, 27, and 28, respectively.
Who is telling the truth?”
See The King of the Spiders for a solution.
This is a logical puzzle from Muhammad Zain Sarwar on Puzzle Sphere.
“Real Psychological Puzzle that will Test your Logical Thinking
Only 10% of Participants gave the Right Answer!
Imagine in front of you there are four cards placed on a desk. Each card has a number on one side and a color on the other. The visible faces of the cards show the following:
You are given a rule to verify:
“Every card that shows an even number on one side, then the opposite side must be red.”
Puzzle Statement
Your task is to determine which cards you must flip over to check whether this rule is being followed or not.
This question was part of a real psychological experiment.”
(I emphasized the “must” in the puzzle statement in order to limit the number of cards flipped to the minimum.)
See Logical Card Test for a solution.
Here is another problem from BL’s Weekly Math Games.
“For every point P on y = 2x2, areas A and B are equal. Find the equation for curve C.”
See Mystery Curve Puzzle for a solution
Here is an entertaining puzzle from Futility Closet.
“By Wikimedia user Efbrazil. Begin at the star. The number at your current position tells you the number of blocks that your next jump must span. All jumps must be orthogonal. So, for example, your first jump must take you to the 1 in the lower left corner or the 2 in the upper right. What sequence of jumps will return you to the star?”
See A Number Maze for solutions
