© 2012 Michael Serra www.mserramath@gmail.com 1

Pirate Math Treasure hunt puzzles with

rectangular, polar, and spherical coordinates

CMC-S Palm Springs Fall, 2012

with Michael Serra

© 2012 Michael Serra www.mserramath@gmail.com 2

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1 3 5 7 92 4 6 8

"Dig

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x,y)

X, E

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10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

12

34

1234

-1-2

-3-4

-1 -2 -3 -4

12

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-1-2

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1 3 5 7 92 4 6 8

"Dig

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x,y)

X, E

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10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

© 2012 Michael Serra www.mserramath@gmail.com 3

18P

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X, E

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10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

1 3 5 7 92 4 6 8

"Dig

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X, E

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10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

0°15°

30°

45°

60°

75°

90°

105°

120°

135°

150°

165°

180°

-165

°

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° -135

° -120

° -105

° -90°

-75°

-60°

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0°-15° 0°15°

30°

45°

60°

75°

90°

105°

120°

135°

150°

165°

180°

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° -120

° -105

° -90°

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0°-15°

© 2012 Michael Serra www.mserramath@gmail.com 4

2.9 Buried Treasure Puzzles on a Rectangular Coordinate System On the coordinate grids for puzzles 31 and 32 below, each E represents an edge of a pentomino, each C represents a corner, and an X means the pentomino does not pass through that point. Locate and sketch the pentomino. 31. 32. For puzzles 15-18, the goal is to find all five tetrominoes in each 8x8 grid. Tetrominoes will not occupy adjacent squares, horizontally, vertically, or diagonally. The numbers along the right vertical edge and the bottom edge indicate the number of squares occupied by the hidden tetrominoes in that particular row or column. The five tetrominoes are shaded as shown below.

The one tetromino that has a longest chain of four squares is always shaded dark. The two tetrominoes with a longest chain of three squares have the diagonals of the squares included. The two tetrominoes with longest chains of two squares are always shaded lightly with dots. Occasionally, portions of tetrominoes are shown.

15. h 16.

X0 1 2 3 4 5 6

0

1

2

3

4 X

CCX C

-1

-2

-1

XC

-3

5

7

ECX

1

1

2

-1

-1

2

3

-2

-2

-3

-3

3X

X

X

C

C

C C

C E

5 2 1 0

0134

0 4

32

6 2

52

0 2 4 2

4204

4 3

22

3 2

06

© 2012 Michael Serra www.mserramath@gmail.com 5

3.6 Buried Treasure Puzzles on a Polar Coordinate System In this set of polar buried treasure puzzles your task is to locate all twelve pentominoes in the 7x24 circular grid with no two pentominoes touching, even at the corners. The twelve pentomino shapes are identified by the letters T, U, V, W, X, Y, Z, F, L, I, P, and N. These letters, representing the twelve shapes, are given as clues. If the letter T, for example, is in a region then the T-pentomino covers that region. Use logical reasoning to determine the location of all the pentominoes. PBT Puzzle 14 h PBT Puzzle 15

TUVWXYZFLIPN TUVWXYZFLIPN

4.5 Spherical Buried Treasure Puzzles In this set of spherical buried treasure puzzles you task is to locate two identical buried treasure tetrominoes on the globe given. The two tetrominos are reflections of each other. They are reflected over either the heavy longitude or latitude lines. The two do not touch. Again, a C represents a corner hit, an E represents an edge hit, an I represents an interior hit, and an X represents a miss. The tetrominoes are located completely on the half of the globe shown. 7. 8.

I

I

L

z z

U

PPP

VV

V

X

YY

N

NF F

T

W

I

L

Z

U

P

P

V

V

X

Y

N

N

F

W

L

T

L

CC C

X XI

© 2012 Michael Serra www.mserramath@gmail.com 6

6.2 Finding Pirate Treasure with Coordinate Geometry Clues In this section you will be using your coordinate geometry skills to locate pirate treasure on ten different tropical isles. You might wish to review some properties of Cartesian coordinate geometry in Appendix II. Each island has a coordinate grid overlay but the origin is hidden. Your first task will be to solve a mini-puzzle to locate the origin and then use your coordinate geometry skills to locate the buried treasure.

10.   Buried  Treasure  on  Isla  Tortuga  • Think of a fifth word that forms a new word or familar two word phrase with each of the following

sets of words. For example:{bug, cover, flower, fellow}. The word that can be attached either before or after is bed. After filling in the blanks and boxes for each of the six words, arrange the nine letters in the boxes into two words for the origin of the coordinate grid on Isla Tortuga.

{style, jacket, love, wild}: __ __ __ {bitter, potato, tooth, talk}: __ __ __ __ {contest, mark, sleeping, shop}: __ __ __ __ __ {walk, cup, beef, hot}: __ __ {hound, slide, bed, sham}: __ {bird, sick, true, seat}: __ __ __ Therefore the origin is located at

• The treasure is located at the circumcenter of the triangle formed by Turtle Rock, the gallows, and the point (8, -1). What are the coordinates of the treasure location?

© 2012 Michael Serra www.mserramath@gmail.com 7

6.3 Finding Pirate Treasure with Polar Coordinate Clues In this section you will be using your polar coordinate geometry skills to locate pirate treasure on six different tropical isles. You might wish to review some properties of polar coordinates in Appendix X. Each island has a polar grid overlay with the origin located at the island gallows. The concentric circles are each ten paces apart. Your first task is to solve a mini-puzzle to locate the starting point of your treasure hunt. Next, use your polar coordinate skills to locate the buried treasure.

3.   Buried  Treasure  on  Isla  Plata  • The location of the starting point is found by arranging the letters in each

column in the lower 7x6 grid into the empty squares of each corresponding column in the upper 7x6 grid and then read the message horizontally.

• From your starting point send one pirate mate walking in the direction of the gallows for 90 paces. Drive a stake in the ground and label the point P.

• From point P move 30° clockwise staying the same distance from the gallows. Drive a stake in the ground and label the point Q.

• The treasure is buried 60 paces from the gallows and at a point T such that PT = QT.

• What are the coordinates of all the possible treasure locations?

a ic kl op os ry

a cc ii nt ou rt

ant

c ag aj es iv t

© 2012 Michael Serra www.mserramath@gmail.com 8

6.4 Finding Pirate Treasure with Geometry Clues In this section you will be using your geometry skills to locate pirate treasure on tropical isles. You will need a compass, straightedge, ruler, protractor, and perhaps patty paper or tracing paper. You might wish to first review some properties of geometry in Appendix X.

8.   Buried  Treasure  Hunt  on  Isola  Diavolo  You find an old treasure map that gives clues to the location of a treasure chest buried on Isola Diavolo. The map shows the debtor's prison and a giant boulder in the shape of the devil. The treasure is located at a point that forms an isosceles right triangle with the debtor's prison gate and the Devil's Boulder. Find the treasure.