500: Secret Salary

My employer has nine workers. The nine of us want to determine what our average salary is, but none of us wants to divulge his own salary. Can we find the average without doing so?

source.

477: How Many Knots?

from NCTM:

How many knots will form if you pull the ends of the string in opposite directions?

470: Poor Alex Bellos

Normally, I'm glad when the nedia talks about math, even if it is simply the latest "Super-Hard problem from Asia that All of Us Stupid American Adults and Brits Won't be Able to Solve but Their 8 Year-old Do Routinely."

Throw in "I gave it to a mathematician and he couldn't solve it either" and you've got an instant viral hit, apparently.

All right, rant over.

What's the error?

Oh, and solve it if you want, too. It's not really that hard.

Further questions:

• Which blanks CANNOT have a prime number in them?
• Which blanks COULD have certain prime numbers?
• Which blanks essentially force this problem to be non-unique?

source.
(answer linked from there)

457: Codebreaker

What are the values of the letters that will allow you to go as far as possible?

How high can you go?

Is there a better way to solve this than just marching up the line, and guessing at the values for H, R, then for F, U, then for I, V and so on?

The original is below. Is this the best set of values?

source:

Negative numbers code-breaker activity with a twist! #mathschat #MathsTLP pic.twitter.com/bOrXtB7mzS

— MathedUp! (@MathedUp) May 10, 2015

448: Hexagon Puzzle

Why did the puzzle creator only ask for circles A and B?

In the diagram, the 19 circles are to contain the integers 1 to 19 once each.
The sum total along any of the lines is 38.
Determine the integers in circles A and B.

Can you find the rest of the circles, too?


Another puzzle from Five Triangles.

435: Interesting Question from NCTM Boston

Interesting question. #NCTMBoston pic.twitter.com/Jco11RaesK
— Steve Wyborney (@SteveWyborney) April 18, 2015

414: Special Right Triangles

#mathsTLP Really must share this... Pythagoras meets surds - what's so special about these triangles? Higher GCSE pic.twitter.com/0v8vB6dEW4
— James Pearce (@MathsPadJames) March 22, 2015

375: Pencils and Jars

373: Product Puzzle 4

For the last couple of days, I've been asking you to create a new puzzle. Today, I'd like you to describe HOW to create a puzzle with a unique solution, or two solutions, or three. How did Don Steward create these and KNOW that they only had one solution?

source.

372: Product Puzzle 3

Put algebraic expressions into the cells so that the product is as indicated. That's for warm-up.

That's not what I'm going to ask you to do, though ...

Make a new puzzle with two solutions.

source.

371: Product Puzzle 2

Put integers into the cells so that their product is as indicated. But that's not what I'm going to ask you to do, though ...

Make a puzzle with exactly 3 solutions.

source.

370: Product Puzzle

Put integers into the cells so that their product is as indicated.
source.

368: Number Puzzle

source.

267: Date puzzle

The day before yesterday Edward was 17.  Next year he will be 20.  How can that be the case?

266: Lending $50

If I were to give you $50 we'd have the same amount. If you were to give me $50 I'd have 9 times as much as you. How much do we each have?

Source.

259: Another Sets Puzzle

There are 40 students in the Travel Club. They discovered that 17 members have visited Mexico, 28 have visited Canada, 10 have been to England, 12 have visited both Mexico and Canada, 3 have been only to England and 4 have been only to Mexico. Some club members have not been to any of the three foreign countries and an equal number have been to all three countries. How many students have been to all three countries?

Source: UVM, 2011

242: Trapezoid Puzzle

figure not drawn to scale.

An isosceles trapezoid has the following properties:

Leg = 30
Diagonal = 82
The difference of the bases is 48

Find the area of the figure.

213: Oh, Now it's you, Chocolate?

I'm getting pretty annoyed.

212: Hold on there, Triangle

Take a moment to find the areas of both triangles. Check that the pieces of both triangles are the same shapes and sizes.

What topic in algebra I is a really good way to explain this?

211: Wait a Minute, Square.

Take a moment to check that each piece in the top diagram is identical to its counterpart in the bottom one.

If you want to recreate this in Geogebra ...

1. turn on grid.
2. insert the polygons in this order: green triangle, black rectangle, yellow L-shape.
3. insert a segment up the "middle" at the appropriate x-position.
4. locate the intersection point of the segment and the hypotenuse of the triangle.
5. insert the two final polygons.
6. Click on each polygon, and copy-paste and build the second figure below the first one.