Puzzles and Recreational Math

Developing Perseverance for Problem Solving while

Having Fun!

Break All RectanglesChallenge 1: How many rectangles of all possible sizes can you find in this diagram? Rectangles are found by locating four dots that lie at the rectangle’s corners.

Challenge 2: What is the least number of stars you must remove so that no rectangles remain in the diagram?

Twin Triangles

Six toothpicks make two equilateral triangles. Move two toothpicks to make four equilateral triangles. (Toothpicks may be overlapped.)

Triangle Areas: Ascending

Can you place these four triangles in the ascending order of their respective areas?

What’s In The Square?

What should be drawn instead of the question mark in the empty square to make the pattern complete?

Extra Square

Move four matchsticks to form three squares.

Straight as an Arrow

Without lifting your pencil off the paper, draw a closed loop of five straight line segments passing once through the center of each of the twelve dots.

7 = 5 Equality

Move three sticks to make a correct equation.

Flower Petals

Which letters should replace the two question marks on the flower petals and why?

Quadrilateral Areas: Odd One Out

One of these four quadrilaterals has a different area than the other three. Which one?

Squares: 8 to 11

Six identical squares are arranged into a 2 x 3 rectangle. Eight different square outlines can be seen in it. Rearrange the squares so that 11 square outlines appear.

X < X ?

Obviously, X cannot be less than itself. Move one stick to another position to make a correct statement.

Forest Figures

Similar to a cryptogram, each digit in this sum has been consistently replaced with a different letter. Can you replace all the letters to make the sum correct?

Ice Cream Trisection

Cutting along the lines of the grid, divide the shape into three congruent parts.

III + II = IIII ?

Move two toothpicks to form a correct equation.

Quadro Cut

Divide the shape into four

congruent parts.

Quadrilateral Area: Pairs

Distribute the four quadrilaterals into two pairs containing shapes of the same area.

The Mountain

Using the three line segments shown, divide the triangular shape into two parts of the same area. Each segment is the same length as one of the long sides of the small triangular cells.

Place all three line segments only along lines of the grid.

Twin Time

You have a 24-hour clock whose display always shows four digits. That means it displays times from 00:00 (exactly midnight, or 12:00 AM) to 23:59 (one minute before midnight, or 11:59 PM).

For the purposes of this puzzle, let’s call a time when the hours and minutes of the clock display the same time (such as 12:12) as a “twin time.” How many times during a single 24-hour period will such “twin times” occur?

The Butterfly

Using the three line segments shown, divide the butterfly into multiple sections according to the following rule:

Two parts of the same area and the same shape.

Always ThreeSix identical coins are arranged into an inverted pyramid, as shown in the left position. This shape contains three rows of three coins. Moving one coin at a time, turn the pyramid 180 degrees to reach the position shown at the right. There’s one complication, though: After each move, the position of the coins must still contain exactly three rows of three coins each.

Start

Finish

“Big D”

What letter and number should replace the question mark in order to complete the sequence around the D?

Triple Division

Divide this figure into three congruent parts.

1 = 4?

Move two toothpicks to make the equation correct.

Seven Cube Distance

This shape consists of seven identical 1 x 1 x 1 cubes. What is the distance between the two black dots (at two cubes’ corners?)

Not So Easy Chair

Cutting along the lines of the grid, divide the chair shape into three congruent parts.

Change the Total

Reading from left to right, these two digits can be read singly or together as three numbers: 6, 3, and 63. Adding 6+3+63 gives a total of 72. Move one toothpick to make two digits that, when interpreted the same way, make a sum of 73.

Triangular Stripes

How many outlines of triangles of all sizes can you trace in the pattern?

Choco-break

Break the chocolate bar into four congruent pieces. Each break must be made along a single straight line running from edge to edge of the bar or an already separated fragment.

Ad Algebra

One day an webmaster logged in to look at the ad revenues from his site. His account showed, “Today’s Earnings” as $0.01, “Yesterday’s Earnings” as $1.33, and “This Month’s Earnings” as X.

The very next day the webmaster logged on once again. This time, “Today’s Earnings” was $0.04, while “Yesterday’s Earnings” was $1.51, and “This Month’s Earnings” was now $9.69. Given that both days were in the same month, can you determine the value of X?

01

2

3

45

6 9

8

7

Table Tetrasection

Cutting along the lines of the grid, divide the shape into four congruent parts. Can you find

two different solutions?

Increasing Time

You have a 24-hour clock whose display always shows four digits. That means it displays times from 00:00 (exactly midnight, or 12:00 AM) to 23:59 (one minute before midnight, or 11:59 PM).

For the purposes of this puzzle, let’s call a time when the clock displays four digits that make an increasing arithmetic progression (such as 12:34) with an increasing constant of 1 an “increasing time.” How many times during a single 24-hour period will such “increasing times” occur?

Eight Cube Distance

This shape consists of eight identical 1 x 1 x 1 cubes. What is the distance between the two black dots (at two cubes’ corners?)

Change the Total 2

Reading from left to right, these two digits can be read singly or together as three numbers: 9, 9, and 99. Adding 9+9+99 gives a total of 117. Move one toothpick to make two digits that, when interpreted the same way, make a sum of 99.

Letter Relations

What letter should replace the question mark in order to logically complete the complex equation?

E D N ?R S U W

Two T’s

Four rectangular times make two T’s, as shown below.

Challenge 1: Moving the fewest pieces, make three T’s.

Challenge 2: The same as above, but make four T’s.

Nine Cube Distance

This shape consists of nine identical 1 x 1 x 1 cubes. What is the distance between the two black dots (at two cubes’ corners?)

Checkered Outlines

How many outlines of squares of all sizes can you find in this pattern?

3 x 3 Reduction

If the length of each matchstick is “a”, then the area of this square is 9a2. Can you move four matchsticks in order to change the square into a shape with the area 6a2? How about moving five matchsticks to make a shape with the area 3a2?

Triangle Areas: Two out of Five

Two of these five triangles have the same area. Which ones?

23 versus 32

The two missing digits in this sequence are 2 and 3. (For now, their places are being held by question marks). But don’t write them in just yet! We haven’t told you in what order they should go. Should the first question mark be

replaced with 2 and the second one with 3, or vice versa?

8, 5, 4, 9, 1, 7, 6, ?, ?

Product Placement

Similar to a cryptogram, each digit in this sum has been consistently replaced with a different letter. Can you replace all the letters to make the sum correct?

Get Less

Obviously, 3 x 3 is 9. Can you move two matchsticks to make an expression equal to 5 instead?

Coin Cup

Eight coins are arranged in the shape of a cup. Move two coins to new positions to turn

the cup upside down.