How many different kinds of polygons can you make by slicing a polyhedron?

What 3D shape has triangular and hexagonal cross-sections? Figure it out by imitating an MRI.

Unfolding a 3D shape shows its surfaces from a different perspective. What's the shortest path between opposite corners of this room?

There are 11 different nets that fold into cubes. In this challenge, the net faces are colored so that only one can make the target cube.

A cuboctahedron can be created by cutting the corners from a cube. After doing this, which faces are have more surface area?

Two ants are taking leisurely trips to the top of a can, but with the shortest possible paths. How much farther does one ant go?

A cross-section of a 3D shape is its intersection with a plane. What does it look like when you move this plane?

Unfolding a 3D shape shows its outer surfaces from a different perspective. Which ant's path is shorter?

Some 3D shapes have similar cross-sections. Can you compare how the cross-sections change to identify the solids they come from?

Unfolding a 3D shape shows its outer surfaces from a different perspective. Which ant's path is shorter?

Reasoning about how the parts of a 3D shape are connected can help us count the parts.

Polyhedra are made from faces, edges, and vertices. Reasoning about how the parts are connected can help us count them.

If we unfold this box, we can find the shortest path from one corner to another. Is it shorter than a walk around the base?

Some Grid Fill puzzles have multiple solutions. Can you use one solution to find others without starting over from scratch?

Solving a Grid Fill puzzle involves logic with arithmetic. For some puzzles, more than one solution is possible.

It can be helpful to start by focusing on the most restrictive conditions.

When solving puzzles, it's often helpful to start by focusing on the most restrictive conditions.

Use logic and arithmetic to discover if there is more than one arrangement of numbers that works.

Building a right triangle is easy, but what if all the sides have to be integer lengths?

Some operations can't be easily undone, and mixing together two colors of sand certainly qualifies as one of these. What happens when we try to "undo" the mixing by transferring some material back into the original container?

Different people work at different speeds. Can you infer how much time will Robert need to complete the task?

Runners don't all accelerate at the same rate and number sequences can act in the same way. Which of these sequences ultimately wins?

To solve a Grid Fill puzzle, you need to arrange tiles so their sums match the required values. How does a negative tile help you balance things?

The values of the tiles in this Grid Fill puzzle double as they get larger. Does that make finding the tiles for each sum easier?

Not all Calcdoku puzzles have a unique solution. For this puzzle, is there exactly one solution, or are there more?

Make sure all the conditions are satisfied as you sort numbers into the correct boxes in this puzzle.

Make each row and column sum to the correct value to solve this Grid Fill puzzle.

The average speed isn't just the arithmetic average of speeds. Don't forget about it when solving today's challenge.

In this Grid Fill puzzle, all of the tiles are prime and four of the sums must be prime as well. Then what is the value of the final sum?

Make the rows and columns add up to the correct values to finish this grid fill puzzle. How many solutions can it have?

Use negative numbers to make the rows and columns add up to the correct values in this Grid Fill puzzle.

Solving a Calcdoku puzzle requires logic and arithmetic. In this one, the arithmetic focus is subtraction and division.

Sometimes, we can rearrange the numbers in a grid so that every row and column has the same sum. Instead, could we make this sum by replacing numbers with 0s?

Grid Fill puzzles are solved by making their rows and columns add to certain values. What's the largest possible product of a row in this puzzle?

In this Grid Fill puzzle, all of the tiles are prime and four of the sums must be prime as well. Then what is the value of the final sum?

Number Bunchers puzzles are solved with arithmetic and logic. Can this one be answered without completely solving the puzzle?

Solving a Grid Fill puzzle involves logic and arithmetic. For some puzzles (including this one) more than one solution is possible.

Number Bunchers puzzles all involve arithmetic and logic. This one asks you to form numbers by putting tiles together as digits.

Calcdoku puzzles don't allow repeat digits in any row or column, but repeats can happen in differently shaped regions.

Hexagons are made out of triangles. Can you use this fact to solve a problem about a number sequence?

Make each row and column sum to the correct value to solve this Grid Fill puzzle.

Some numbers can be multiplied more quickly with a little algebraic reasoning than by using a calculator. Can you use a similar idea to efficiently divide, too?

In this balance puzzle, exact weights are less important than relationships among them. Which side of the scale is heavier?

When step-by-step calculation would be tedious or time-consuming, we look for other approaches. Can you shortcut past the subtraction in this problem?

One way to visualize an equation is as a carefully balanced scale. As long as we only do things that keep both sides in balance, we can add, remove, and substitute freely...

In a magic square, the sums of every row, column, and diagonal are equal. What happens in a multiplication magic square?

When thinking about percentages and ratios, we shouldn't always trust our intuition. To solve today's challenge, you might need to do some careful computations.

When step-by-step calculation would be tedious or time-consuming, we look for other approaches. Can you shortcut past the subtraction in this problem?

One difference between Grid Fill and Sudoku puzzles is that Grid Fill can have multiple solutions. How many solutions does this puzzle have?

Have you ever wondered why all surface area formulas have x or r squared in them somewhere, and all volume formulas contain x or r cubed? N-dimensional reasoning trumps memorizing formulas every time!

Finding the numerical equivalent of each shape can get a little messy. Switching out shapes and balancing might help to keep things tidy.

This Calcdoku puzzle has more than one solution. What can you say about how the solutions are related?

Each person pays in a different amount, but they all get the same amount at the end. Or do they?

Sometimes a sequence is almost a geometric progression, but not quite. What's the next term in this sequence?

Thinking about a special kind of sum might make solving this puzzle quicker.

Mixing up a precise recipe requires carefully balancing the amounts of each ingredient. Organize your thoughts precisely, or it will all get muddled up!

Can a Symmetric Process Lead to an Asymmetric Outcome?

Keep track of the candies in this puzzle closely… of course, they’re digital, but they’re still apt to disappear if you’re not careful!

The terms of the Fibonacci sequence grow larger and larger. What patterns lie inside?

Can you find a general formula for the perimeter of a row of polygons?

The terms of some sequences can be very tedious to calculate and add up. Sometimes a geometric approach might help.

How much information do you need to find the weight of the circle?

Small cubes are put together to form a larger cube, and then the outside gets painted. How many of the small cubes get painted on only one or two sides?

When two regular polygons intersect, they define new regions. What's the maximum number of regions for a given pair?

Finding the numerical equivalent of each shape can get a little messy. Switching out shapes and balancing might help to keep things tidy.

Algebra can help uncover how this number pattern works. Can you figure out when it stops working?

A balanced scale stays balanced if we add or remove equal quantities from both sides. Can you solve this balance puzzle?

Grid Fill puzzles are solved by making the rows and columns add to certain values. Which set of numbers isn’t used to sum to 9?

Calcdoku is a game of logical reasoning. What numbers will successfully fill the grid?

Solve this Calcdoku puzzle using careful logic and attention to the properties of arithmetic.

How many circles will balance a square and a triangle?

Adding or removing the same quantity on both sides of a balanced scale keeps it balanced. What can you do to solve this balance puzzle?

By analyzing two balanced scales, we can understand the relationships among different weights. Are the other two scales balanced?

Can you find the relationship between weights of the circle and the triangle?

To balance this scale, we need to add an extra weight. What weight should we place and on which side?

Calcdoku puzzles challenge you to reason with arithmetic. Try focusing on factors when solving this 5 x 5 puzzle.

Calcdoku puzzles are solved using logic with arithmetic. Solve a 5 x 5 puzzle for this challenge.

Solving a Calcdoku requires logic as well as arithmetic. When it looks like information is missing, can you imagine what isn't there?

Balanced scales tell us something about the relationship among weights of different shapes. Can you find the heaviest one?

In 2019, resolve to learn math so that it makes sense, be it via geometric, algebraic, or logical reasoning...

Systems of equations can look complicated—after all, there are several equations involved. However, the process of elimination can reduce a large problem to a small one.

A balanced scale stays balanced if we add or remove equal quantities on both sides. Can you balance two squares?

Calcdoku puzzles look similar to Sudoku puzzles, but they have arithmetic rules built in. For this one, try to fill the elbow-shaped regions.

Subtracting different squares don't cancel entirely, but they certainly take a piece out of each other. What happens when we repeat the process?

Constraints can help us eliminate cases when solving problems. Which constraint is the most helpful in this puzzle?

If you've done a problem wrong, do you need to start over from the beginning? Not if the problem involves multiplication.

Adding or removing the same quantity on both sides of a balanced scale keeps it balanced. What will balance with three squares?

Small cubes are put together to form a larger cube, and then the outside gets painted. How many of the small cubes get painted on only one or two sides?

Can you figure out what numbers go into the second row?

There are many ways to solve systems of equations, but often one is more efficient than others…

Finding the numerical equivalent of each shape might not be possible. Switching out shapes and balancing will solve this puzzle.

Use a combination of logic and arithmetic to find the middle row of this Calcdoku puzzle.

There are a few patterns hidden in this figure; can any of them make solving the challenge easier?

Use logic and arithmetic to fill in this Calcdoku puzzle. Can you find the solution?

Can you deduce how many triangles will balance the circles?

Calcdoku puzzles require not just arithmetic but also logic. If you know where a number can't go, can that determine where it must belong?

Use logic and arithmetic to move the pyramid of tiles to the pyramid of squares.

A scale is balanced if the weights on each side are equal. Given two balanced scales, can you determine if the third one is balanced?

Balance puzzles are a helpful visual tool for thinking about equations. Can this one be solved?