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# Recreational Math Puzzles

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Source: The Big, Big, Big Book of Brainteasers, by the Grabarchuk family. Puzzles like these can be used to help students develop perseverance (MP1).

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### Recreational Math Puzzles

1. 1. Puzzles and Recreational Math Developing Perseverance for Problem Solving while Having Fun!
2. 2. Break All RectanglesChallenge 1: How many rectangles of all possible sizes canyou find in this diagram? Rectangles are found by locatingfour dots that lie at the rectangle’s corners.Challenge 2: What is the least number of stars you mustremove so that no rectangles remain in the diagram?
3. 3. Twin TrianglesSix toothpicks make two equilateral triangles. Move twotoothpicks to make four equilateral triangles. (Toothpicksmay be overlapped.)
4. 4. Triangle Areas: AscendingCan you place these four triangles in the ascending orderof their respective areas?
5. 5. What’s In The Square?What should be drawn instead of the question mark in theempty square to make the pattern complete?
6. 6. Extra SquareMove four matchsticks to form three squares.
7. 7. Straight as an ArrowWithout lifting your pencil off the paper, draw a closed loopof five straight line segments passing once through thecenter of each of the twelve dots.
8. 8. 7 = 5 EqualityMove three sticks to make a correct equation.
9. 9. Flower PetalsWhich letters should replace the two question markson the flower petals and why?
10. 10. Quadrilateral Areas: Odd One Out Odd One OutOne of these four quadrilaterals has a different areathan the other three. Which one?
11. 11. 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.
12. 12. X < X?Obviously, X cannot be less than itself. Move onestick to another position to make a correctstatement.
13. 13. Forest FiguresSimilar to a cryptogram, each digit in this sum hasbeen consistently replaced with a different letter.Can you replace all the letters to make the sumcorrect?
14. 14. Ice Cream TrisectionCutting along thelines of the grid,divide the shapeinto threecongruent parts.
15. 15. III + II = IIII ?Move two toothpicks to form a correct equation.
16. 16. Quadro Cut Divide theshape into four congruent parts.
18. 18. The MountainUsing the three line segmentsshown, divide the triangularshape into two parts of thesame area. Each segment isthe same length as one of thelong sides of the smalltriangular cells.Place all three line segmentsonly along lines of the grid.
19. 19. Twin TimeYou have a 24-hour clock whose display always shows fourdigits. That means it displays times from 00:00 (exactlymidnight, 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 thehours and minutes of the clock display the same time (suchas 12:12) as a “twin time.” How many times during a single24-hour period will such “twin times” occur?
20. 20. The ButterflyUsing the three linesegments shown, dividethe butterfly into multiplesections according to thefollowing rule:Two parts of the samearea and the sameshape.
21. 21. Always ThreeSix identical coins are arranged into an inverted pyramid, as shownin the left position. This shape contains three rows of three coins.Moving one coin at a time, turn the pyramid 180 degrees to reachthe position shown at the right. There’s one complication, though:After each move, the position of the coins must still contain exactlythree rows of three coins each. Start Finish
22. 22. “Big D”What letter and numbershould replace thequestion mark in order tocomplete the sequencearound the D?
23. 23. Triple DivisionDivide this figureinto threecongruent parts.
24. 24. 1 = 4?Move twotoothpicks tomake theequationcorrect.
25. 25. Seven Cube DistanceThis shape consists of sevenidentical 1 x 1 x 1 cubes.What is the distance betweenthe two black dots (at twocubes’ corners?)
26. 26. Not So Easy ChairCutting along the linesof the grid, divide thechair shape into threecongruent parts.
27. 27. Change the TotalReading from left to right,these two digits can be readsingly or together as threenumbers: 6, 3, and 63.Adding 6+3+63 gives a total of72. Move one toothpick tomake two digits that, wheninterpreted the same way,make a sum of 73.
28. 28. Triangular StripesHow many outlines of triangles of all sizes can you trace in the pattern?
29. 29. Choco-breakBreak the chocolate bar intofour congruent pieces. Eachbreak must be made along asingle straight line runningfrom edge to edge of the bar oran already separatedfragment.
30. 30. Ad AlgebraOne day an webmaster logged in to look at 4 5the ad revenues from his site. His accountshowed, “Today’s Earnings” as \$0.01,“Yesterday’s Earnings” as \$1.33, and “This 2Month’s Earnings” as X. 8The very next day the webmaster logged on 1 0once again. This time, “Today’s Earnings”was \$0.04, while “Yesterday’s Earnings” was\$1.51, and “This Month’s Earnings” was now 3 9\$9.69. Given that both days were in thesame month, can you determine the value ofX? 6
31. 31. Table Tetrasection Cutting along the lines of the grid, divide theshape into four congruent parts. Can you find two different solutions?
32. 32. Increasing TimeYou have a 24-hour clock whose display always shows fourdigits. That means it displays times from 00:00 (exactlymidnight, 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 theclock displays four digits that make an increasing arithmeticprogression (such as 12:34) with an increasing constant of 1an “increasing time.” How many times during a single 24-hour period will such “increasing times” occur?
33. 33. Eight Cube DistanceThis shape consistsof eight identical 1 x1 x 1 cubes. Whatis the distancebetween the twoblack dots (at twocubes’ corners?)
34. 34. Change the Total 2Reading from left to right,these two digits can be readsingly or together as threenumbers: 9, 9, and 99.Adding 9+9+99 gives a total of117. Move one toothpick tomake two digits that, wheninterpreted the same way,make a sum of 99.
35. 35. Letter RelationsWhat letter should replace the question markin order to logically complete the complexequation? E D N ? R S U W
36. 36. Two T’sFour 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.
37. 37. Nine Cube DistanceThis shape consists of nineidentical 1 x 1 x 1 cubes.What is the distance betweenthe two black dots (at twocubes’ corners?)
38. 38. Checkered OutlinesHow many outlines ofsquares of all sizescan you find in thispattern?
39. 39. 3 x 3 ReductionIf the length of eachmatchstick is “a”, then thearea of this square is 9a2.Can you move fourmatchsticks in order tochange the square into ashape with the area 6a2? Howabout moving five matchsticksto make a shape with the area3a2?
40. 40. Triangle Areas: Two out of FiveTwo of these five triangles have the same area. Which ones?
41. 41. 23 versus 32The two missing digits in this sequence are 2 and 3. (Fornow, 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 bereplaced with 2 and the second one with 3, or vice versa? 8, 5, 4, 9, 1, 7, 6, ?, ?
42. 42. Product PlacementSimilar to a cryptogram, each digit in this sum hasbeen consistently replaced with a different letter. Canyou replace all the letters to make the sum correct?
43. 43. Get LessObviously, 3 x 3 is 9. Can you move twomatchsticks to make an expression equal to 5instead?
44. 44. Coin Cup Eight coins are arranged in the shape of acup. Move two coins to new positions to turn the cup upside down.