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There is a yellow smiling face in the center. There is a green border around the outside.

Smileys

Gray box with red and blue dots and a question mark. There's a red border around the images.

Crack the Code

There are two squares in the center of the image. The square on the left is smaller than the square on the right. Both squares are rotated about 45 degrees so that one of their vertices is facing downward. The squares partially overlap in the middle. The squares are white with a green border; the overlapping area is green. There is a blue border around the images.

Mysterious Areas

There are four balls stacked so that there are 3 balls on the bottom and 1 ball on top. The ball on top is green. From left to right, the three balls on the bottom are blue, orange, and black. There is a green outline around the images.

Dimensions

A brown chocolate bar with 2 rows and 4 columns of square chocolate pieces. The bottom left square is red with a yucky face. There's a green outline around the image.

Chomp

There are 12 triangles that are arranged to make 2 hexagons that are side-by-side horizontally. The triangles on the left are different shades of purple. The triangles on the right are different shades of red. There is a yellow border around the images.

Hexaflexagons

A map of a town with houses, stores, lakes, and a baseball diamond is in the center. Along the roads, there are arrows that show which direction the townspeople can go at intersections. On the left, there is a policeman writing a ticket to a woman in a red car.

A Tribute to Robert Abbott

There are 8 parallelograms in a row. From left to right, the parallelograms alternate between light red and dark red. The parallelograms are adjacent to one another in such a way that they create a zig-zag line along the top and bottom of the image. This gives the illusion of a folded piece of paper. There is a yellow border around the images.

Folding Fractals

There are three black-and-white penguins standing side-by-side in a row. The penguins have an orange beak and orange feet. There is a green border around the outside.

Penguin Island

There is a red rectangle in the center with three green poles sticking vertically upwards. On the middle pole, there is a side-view of five disks. Each disk is a different size, that go from largest to smallest from the bottom of the post to the top. From bottom to top, the colors of the disks are pink, orange, yellow, light blue, and purple. There is a light blue border around the outside.

Tower of Hanoi

There is a cover of a light purple booklet. There are 8 images on the booklet arranged in 3 columns. In the left column from top to bottom, there is a stack of red and white disks labeled Arithmetic Series, the steps of a staircase labeled with the numbers 9 through 13 labeled 105, and a timer labeled Egg Timer. In the middle column from top to bottom, there is an image of two police officers labeled Tax Man and a black-and-white photo of skyscrapers from above labeled Skyscrapers. In the right column, there is a red 51 in a red circle labeled Sum of 51, a black 7 on a yellow background labeled How Many 7's, and a photo of a marching band wearing red outfits labeled Marching Band.

Good Problems

There is a yellow square on the left. On the right, the yellow square has been divided in many, different-sized squares using straight blue lines. There is a blue arrow in the middle that points to the right. There is a blue border around the outside.

Squareland

A two-row array with numbers one through ten. There is a blue outline around nine and ten and a green boarder around the full array.

Countdown

A brown, wooden boat floats on top of wavy water in different shades of blue. There is a red border around the outside.

River Crossings

There are three green ovals in a row in the center. On the green oval on the left, there is a yellow, upside-down solo cup. On the green oval on the right, there are two, upside-down solo cups stacked on one another. The cup on the bottom is orange and the cup on the top is red. There is red arrow along the bottom of the green ovals that hops from the right oval, to the middle oval, to the left oval. There is a red border around

Cup Stacking

Squares, triangles, and circles cut into various pieces on a tan background

Halving

There is a white, equilateral triangle with a black outline in the center. The triangle is pointed upwards. On each vertex, there is a colored circle. The bottom-left circle is green, the bottom-right circle is red, and the top circle is blue. There are four, smaller, yellow circles inside the triangle, spaced out asymmetrically. There is a thin black line connecting the left-most, yellow circle with the green circle. There is a green border around the images.

Criss Cross

There is a grid of squares in the center with 7 rows and 7 columns. The squares alternate in color between red, blue, yellow, and green. In each square, there is a number from 1 to 6. In upper left corner, there is a woman jumping next the word start. In the bottom right corner, there is a trophy next to the word finish.

Jumping Julia Printable 2

There is a row of 7 squares in the center of the image. The left 4 squares are green, the right-most square is red, and the two squares in the middle are yellow. There is an equation above the squares that reads 7 equals G Y R. 7 and the equal sign are black, the G is green, the Y is yellow, and the R is red. There is a red border around the images.

Measuring Sticks

There are three grids of squares, where each grid contains squares of different sizes. The left grid contains 3 blue and 1 green squares, where the blue squares are smaller than the green square. The middle grid contains 1 red, 2 yellow, 2 green, and 7 blue squares. The last grid contains 1 yellow and 2 blue squares. Blue squares are the smallest, then yellow, then green, and then red. There is a red border around the outside.

Squareland Architect

There is a grid of squares with 2 rows and 3 columns. On the edges of adjacent squares, there are red bidirectional arrows. There is a red border around the images.

Square Dance

There are five curved arrows arranged in a circle so that each arrow is pointing to the next arrow in the circle. Starting at the top arrow and moving clockwise, the arrows are colored green, red, blue, green, and blue. There is a red border around the outside.

Colored Loops

A kangaroo hopping along the top with different geometric shapes in many different colors along the bottom.

Hopping Mad Patterns

There is a row of three white squares with black outlines. On the left square, there is a triangle on top. In the middle square, there is an X that connects the corners of the square. On the right square, there is both a triangle and an X. There is a light blue border around the outside.

Königsberg

There is a diagonal line of 7 lightbulbs that go from the top left corner to the bottom right corner. The third lightbulb from the left is yellow indicating that it is turned on. All of the other lightbulbs are white. There is a light blue border around the outside.

Lightbulbs

Nebraska, Iowa, Missouri, and Kansas in blue, yellow, and green.

Map Coloring

There is a map of a town with stores and houses on green grass. In between the buildings, there is a road network. At each intersection, there is a red octagon. There is the word start on the bottom left with an arrow pointing up. There is the word finish on the bottom right with an arrow pointing down.

Red Sign Turn

There is a smiling skeleton on the left with yellow eyes. There is a smiling purple bat with yellow eyes on the right. There is a green border around the outside.

Monster Town

Four squares in a 2 by 2 grid, colored red, green, yellow, and blue, labeled 4, 1, 2, and 3, and surrounded by a red border

Jumping Julia

There is a row of 4 circles. From left to right, there is a blue circle, a yellow circle, a white circle with a dotted outline, and a blue circle. There is a red border around the outside.

Blue Dot Solitaire

There is a baseball diamond in the center. The baseball diamond is made of a downwards-facing triangle with a semi-circle on top. The bases are white, the infield is green, and the outfield is yellow. There is a die in the lower left-hand corner with three of its faces showing: a five pointing to the left, a one pointing to the right, and a three pointing upwards. There is another die in the bottom right corner with three faces showing: a six to the left, a four to the right, and a two upwards. The faces of the dice are white, and the pips on the dice are green. There is a green border around the images.

Probability Baseball

There are three white circles with blue outlines in a row. The two outside circles are connected to the middle circle with a straight blue line. The left circle contains an orange 9, the middle circle contains a purple 18, and the right circle contains a green 9. In the upper left corner, there is the equation 9 plus 9 equals 18. In the bottom right corner, there is the equation 1 plus 8 equals 9. There is a red border around the outside.

Digit Sums

There is a network of mostly yellow circles. Some of the circles are connected to one another with black lines. Some of the circles are red and blue. There is a region that touches 3 blue circles and 2 red circles that is itself blue. There is another region that touches 3 red, 2 blue, and 1 yellow circle that is itself red. All other regions are colored white. There is a green border.

Con Hex

On the right, there is a 5 by 5 grid of squares. 14 of the squares are orange and 11 are blue. The colors of these squares make an irregular, sporadic pattern. On the left, there are two larger squares side-by-side. The left square is orange with a white 14 inside. The right square is blue with a white 11 inside. There is a red border around the outside.

Gerrymandering

A rook attacking a queen on a blue and white squared chessboard, surrounded by a red border.

Chess Covers and Tours

A 3x4 array of squares with 1, 2, or 3 pips. Three pairs of squares are outlined in blue as dominoes. The entire image is bordered in red.

Domino Dissection

There are 12 pentagons connected to one another in a way that makes it look like there two 5-petaled flowers connected in the middle. In each pentagon there is a white circle with a black border. The pentagons are white with a black border. There is a yellow border around the outside.

Coloring Solids

There is a simplified 1 dollar bill on the top. Below the dollar bill, there is a row of 7 coins: 3, one cent brown coins on the left, a gray, five cent coin in the middle, and 3, one cent coins on the right. There is a red border around the outside.

Change for a Dollar

There is a beach with water and a palm tree. There is a blue chameleon and a red chameleon on the sand. There is a yellow chameleon in the water. There is a red border around the outside.

Chameleon Island

There are three clear cups in a row. The left cup has purple liquid, the middle cup has green liquid, and the right cup has orange liquid. There is a light blue border around the outside.

Juice Jumble

Five white stars in a pentagram with a blue background.

Fold-and-Cut-Flag

There is a cover of a light blue booklet with 8 images in 3 rows. In the top row from left to right, there is an image of two Hershey kisses labeled Hugs & Kisses, graham crackers labeled Squareable Numbers, and a grid of different-sized squares labeled Squaring Puzzles. In the middle row from left to right, there is a collection of red dots arranged into the shape of a trapezoid labeled Trapezoidal Numbers, a purple and green splash of color on a black background labeled Digit Sums, and a row of lightbulbs with only one turned on labeled Switching Light Bulbs. In the bottom row from left to right, there is an image of two children playing with toys and a boy high-fiving a man.

A Sample of Mathematical Puzzles

There are 6 pieces of chocolate arranged in a grid with 2 rows and 3 columns. In the first row from left to right, there is a brown square, white triangle, and brown circle. In the bottom row from left to right, there is a pink circle, a brown triangle, and a pink square. There is a green border around the outside.

Chocolate Fix

There is a row of 4 circles. From the left to right, the circles are colored red, yellow, red, and red. There is a rounded purple rectangle around and behind the left 3 circles. There is a light blue border around the outside.

Palindrome Grab

There is a field of grass with a network of brown pathways going through it. Throughout the field, there are rocks, purple and orange flowers, turtles, birds, a lizard, a raccoon, an otter, fish, and a lake.

Right Turn Only

There are 10 circles arranged in a downwards-pointing triangle. Circles alternate in color between red, yellow, and light blue. There is a red border around the outside.

Color Triangles

There are three cookie jars in a row with blue lids. There is one chocolate chip cookie in the left jar, two chocolate chip cookies in the middle jar, and three chocolate chip cookies in the right jar. There is a blue border around the outside.

Cookie Monster

There are thee, brown, rounded rectangles in a row. The rectangles are longer than they are wide. Inside each rectangle, there is a column of adjacent, white circles. In the left rectangle, there is a green sugar cookie with sprinkles in the bottom circle. In the middle rectangle, there is a green sugar cookie in the middle circle and a blue sugar cookie in the bottom circle. In the right rectangle, there is a green sugar cookie in the top circle, a blue sugar cookie in the middle circle. and a red sugar cookie in the bottom circle. There is a red border around the images.

Cookie Factory

There is a pool with blue water and tan, man-made islands throughout the water. Towels and life preservers are along the outside of the pool. Red and yellow dots are scattered throughout the blue water. The word start is in the lower left-hand corner, and the word finish is in the lower right-hand corner.

Swimming Around

There is a red ladybug in the middle with two dots on its back and a question mark above its head. This ladybug is in between two green leaves. The left leaf is pointed to the left, and the right leaf is pointed to the right. On the right leaf, there is another red ladybug with one spot on its back.

Ladybugs

A white kitten with black and orange spots is on the left. A brown puppy with white fur on the underside of its stomach and tail is on the right. The animals are staring at one another playfully. There is a green border around the images.

Puppies and Kittens

There is a grid of green squares with 4 rows and 6 columns. There is a white arrow that starts in the bottom left-hand corner, moves in a 45 degree direction northeast, and bounces along three sides of the grid in a 45 degree direction. There is a blue border around the outside.

Billiards Geometry

There are three stacks of dollar bills in different denominations side-by-side horizontally. In the stack on the left, from top to bottom, there is a $4 bill, a $3 bill, a $2 bill, and a $1 bill. In the middle, from top to bottom, there is an $8 bill, a $7 bill, a $6 bill, and a $5 bill. In the stack on the right, from top-to-bottom, there is a $12 bill, an $11 bill, a $10 bill, and a $9 bill.

Tax Collector

A woman jumping to the left of a grid of squares colored in a repeating pattern of red, yellow, green, and blue. Each square has a number from 1 to 4 in it.

Mazes

There is a cover of a light purple booklet. There is an image of three people carrying oversized ballots to a large cardboard box with the word vote written on the front.

Gerrymandering

In the center, there is a cube with black edges. The cube is clear so that the back edges and vertices can be seen. At each vertex, there is a colored circle. Each circle is a different color and is either pink, purple, yellow, green, red, brown, orange, or blue. There is a green border around the outside.

Prime Cubes

There are two purple stick figures looking at one each other and giving each other a high five. Lines are emanating radially away from their high five indicating that it made a loud sound. There is a red border around the outside.

High-Fives

There are three fedoras placed in a row. The left fedora is light brown, the middle one is dark brown, and the right one is blue. Each fedora has a black band. There is a blue border around the images.

Counting: Deranged?

There are three clusters of grapes in a row. The cluster on the left has 3 purple grapes. The cluster in the middle has 6 purple grapes. The cluster on the right has one grape. Each grape cluster has a black stem and a green leaf on the top. There is a light blue border around the outside.

Grape Codes

There is a 4 by 4 grid of white squares that is slanted about 45 degrees counter clockwise. At the top and bottom of each column and to the left and right of each row, there is a colored arrow pointing inwards along the row or column. The arrows alternate in color between red, blue, green, and yellow. There is a red border around the outside.

Skyscrapers

There are two frogs staring at each other. The frog on the left is pointed to the right, and the frog on the right is pointed to the left. The frog on the left is a darker shade of green than the frog on the right, and the frog on the right has spots. There is a red border around the images.

Frogs and Toads

There is a 2 by 4 checkered pattern with light blue and white squares. A black wolf silhouette in a black circle is in the second row, second column square. A black-and-white sheep in a black circle is in the top right square. These images are surrounded by a red border.

Wolves and Sheep

Various red, white, and yellow game pieces on a light blue background

A Mathematician's Travel Kit

Grids, dots, and squares colored in purple and blue on a light blue background

Exploding Dots

There is an image of a white mouse in a black circle on the left. There is a grid of hexagons on the right. The left column of the grid has one tan hexagon. The next column has two tan hexagons. The next column has three tan hexagons. The last column has four green hexagons. The hexagons border each other so that there is no space between them, like in a beehive. There is a green border around the images.

Mousetrap

There is a partial grid of pink squares on the left and a partial grid of green squares on the right. The pink squares are arranged so that there are 4 rows. The top row has 2 squares, the next row has 3 squares, the next row has 4 squares, and he last row has 5 squares. The squares are left-justified. The green squares are arranged so that there are 5 rows. The top row has 1 square, the next row has 2 squares, the next row has 3 squares, the next row has 4 squares, and the last row has 5 squares. The squares are right-justified. There is a light blue border around the outside.

Staircases

There are four, pale green rectangles adjacent to one another in a zig-zag shape. The left-most rectangle has 40 yd2 written inside in black. To the right of this rectangle, there is a rectangle with 80 yd2 written in black. Below this rectangle, there is a rectangle with 90 yd2 written in black. To the right of this rectangle, there is 20 yd2 written in black. Above the rectangle on the far-left, there is a black bracket with 6 yd written above it. Below the rectangle on the far right, there is a black bracket with ? yd written below it. There is a red border around the images.

Farming Fiasco

There are three squares. There is one square on the right that is bigger than the other two squares. The two squares on the left are stacked on top of one another; the square on the top is smaller than the square on the bottom. The two square on the left line up with the left side of the left square; the combined height of the two squares on the left is the same as the height of the square on the right. There is a green two in the smallest square. There is a green 6 in the next smallest square. There is a green 8 in the largest square. In the largest square, there is also the equation 6 plus 2 equals 8 in black symbols.

Jigsaw Squares

Three black circles filled in with blue numbers 0, 2, and 1 connected by black edges labeled with purple numbers 2 and 1 all surrounded by a light blue border.

Graceful Graphs

Two red apples side-by-side. The apple on the left is full and uneaten. The apple on the right has been eaten and is now only the core of the apple. There is a green border around the outside.

Apple Picking

There is a grid of squares in the center with 3 rows and 3 columns. The squares are white with a black border. Two blue, bidirectional arrows lay on top of the grid. One arrow points in the northwest - southeast directions, and the other arrow points in the northeast - southwest directions. There is a red border around the images.

Magic Squares

There is a cover of a light blue booklet. On the cover, there are 6 images arranged in a grid with 2 rows and 3 columns. From left to right and top to bottom, these images are a collection of patterns using dots and lines labeled Wordless Puzzles, an image of an Egyptian pyramid labeled Building a Pyramid, an open, yellow box labeled Folding a Cube, cubes with faces colored red, yellow, and purple and geometric shapes labeled A Puzzling Cube, a 5 by 5 grid of white squares labeled Squares & Cubes, and a tray of muffins labeled The Muffin Puzzle.

Puzzles with Shapes

There are 4 buildings in a 2 by 2 grid. Moving clockwise and starting from the upper left corner, the buildings are red, green, yellow, and blue. There is a road network between and around the buildings. White arrows show the townspeople which directions they can go at intersections. There is a box on the left next to the word start. There is an orange house on the right next to the word finsih.

Delivering Packages

There is a series of three concentric circles in the center. The inner-most circle is white with a black outline. There are black lines connecting the inner-most circle with the middle circle. This creates four, equally-sized regions. There are more black lines connecting the middle circle with the outer circle. This creates six, unequal regions. There is a red border around the images.

Magic Circles

There are 8 carrots in grid with 2 rows and 4 columns. The left two carrots are light orange surrounded by a dark orange, rounded rectangle. The right two carrots are light orange surrounded by a dark orange, rounded rectangle. The top two middle carrots are dark orange and surrounded by a yellow, rounded rectangle. The bottom two middle carrots are dark orange surrounded by a yellow, rounded rectangle. All of the carrots have green leaves on top. There is a light blue border around the outside.

Lots o' Plots

There is a grid of squares with 5 rows and 5 columns. The squares alternate in colors between red, blue, yellow, and green. There are numbers from 1 to 4 in the squares. There is a woman jumping next to the word start in the upper left corner. There is a trophy next to the word finish in the bottom right corner.

Jumping Julia Printable 1

Scissors next to a horizontal dotted line along the top. Different polygon outlines against a pink background.

Fold-and-Cut

There are three rectangles in a row that are more tall than they are wide. In between each rectangle, there is a vertical blue line separating them. The rectangle on the left is separated into 6 segments: one large segment on the top, and five short segments on the bottom. The top-most short segment is colored green. The middle rectangle is separated into 3 equal-sized segments. The top-most segment is green. The rectangle on the right is split into two equal segments. There is a blue border around the images.

Egyptian Mystery

There is a grid of squares with 3 rows and 7 columns. The squares are blue and white, and the grid has a checkerboard pattern. There is a black rook (a playing piece from chess) on the upper right-hand square. A black arrow points from the rook, two squares to the left. Another black arrow points from the rook, two squares downwards. A green border surrounds the images.

Rook's Move

There is a yellow balance scale in the middle. The left pan of the balance scale is blue and the right pan is red. There is a gold bar with the number 1 in the left pan. There is a gold bar with the number 2 in the right pan. The left pan is lower than the right pan. There is a light blue border around the outside.

Panning for Gold

There are four rectangles in a row. The rectangles are taller than they are wide. In order from left to right, the rectangles are blue, green, yellow, and red. There is a red border around the images.

Mind Reading

Four toads on a lilypad. Two of the toads are submerged in water. A blue boarder surrounds them.

Tippy Toads

There is a pile of assorted nuts and violet, purple, and yellow raisins. There is a green border around the outside.

Trail Mix

Graham crackers, a staircase, a grid, a box, graphs, and pitchers on a green background.

Recreational Mathematics (Really!)

$There is a cover of a pale yellow booklet. On the cover, there are images of covers of past Scientific American journals. These images include mathematical patterns like fractals.$

Martin Gardner's Brain Teasers

There is a grid of red squares with 3 rows and 4 columns. A yellow line snakes its way through the red squares so that the line touches goes through the center of each of the squares once. There is a red border around the outside.

Uncut Spaghetti

There is a hamburger on the left, the letters "vs" in the middle, and a salad on the right. A light blue border surrounds these images.

What's for Dinner?

There is a red trapezoid that looks like a fast food container. There are seven, brown chicken nuggets coming out of the top of the container. There is a light blue border around the outside.

Nuggets for Sale

There is a hexagonal grid in the middle of the image. Each hexagon is white with a black outline. The bottom row has one hexagon, the row above that has two hexagons, the row above that has three hexagons, and the row above that has four hexagons. The hexagons border one another so that there is no space between them, like in a beehive. On top of the hexagons, there is a row of five blue circles side-by-side. There are two blue arrows on the sides of the hexagonal grid. The left arrow points in the north-west direction. The right arrow points in the north-east direction. There is a green border around the images.

Random Walks

There are three, rounded rectangles side-by-side. The rectangles are taller than they are wide and are in a similar shape to a playing card. There is one, filled-in purple squiggle on the left card. There are two, striped, green ovals on the middle card. There are three outlines of red diamonds on the right card. A green border surrounds the images.

SET

There are three lab beakers in a row. The left beaker is rounded like a circle, the middle beaker has a triangular shape, and the right beaker is tall and thin. Each beaker contains blue liquid with light blue bubbles. There is a light blue border around the outside.

Pool Testing

There are three rows of mathematical expressions. The top expression says 31 equals 10 times 3 plus 1. The middle expression says equals 9 times 3 plus 3 times 1 plus 1. The 9 and the left-most 3 are purple and crossed out with a red diagonal line. The bottom expression says equals 3 plus 1. There is a blue border around the outside.

Casting Out Nines

There is an underground tunnel network with red and blue dots spread throughout. The tunnels are light gray and the surrounding ground is dark gray. On the left, a miner is standing near the word start. On the right, there is the word finish.

Cave Escape

There is a grid of gray squares with 3 rows and 7 columns. There are two red people in the first column staring to the right. There are three blue people in the last column staring to the left. There are two yellow people in the bottom row, side-by-side, staring upwards. There is a green border along the outside.

Balance Beans

There is a cover of a light orange booklet. On the booklet, there is an image of a grid of colored squares with numbers in them labeled Squaring Puzzles. On the right, there is an image of toy, connecting cubes labeled Skyscrapers.

Puzzling with Squares

A white maze with red, yellow, and green dots on a light blue background.

Robert Abbott Booklet