Grade 10Reading: grades 3-4Pythagorean theoremSquare rootsExponentsOrder of operations

The Mystery of the Sunken Citadel

The golden sun stone has vanished from the Sunken Citadel! The Chief Explorer needs your help to trace clues across the island and catch the sneaky bandit leader.

Suspects

Possible suspects

Cross off a row as each clue rules it out. On screen, tap a row.

21 of 21 still in play

Name	Primary Gear	Bonus Tool	Hand Cover	Hair Style	Defensive Item
Wanderer Will	Grappling Hook	Brass Scope	Wears Gloves	Braided Red Hair	Bright Mirrors
Diver Jack	Glider Pack	Signal Flare	Bare Hands	Sleek Black Hair	Loud Whistles
Captain Avery	Glider Pack	Map Case	Bare Hands	Braided Red Hair	Bright Mirrors
Navigator Elena	Glider Pack	Rope Ladder	Wears Gloves	Braided Red Hair	Loud Whistles
Voyager Uri	Glider Pack	Brass Scope	Wears Gloves	Braided Red Hair	Water Sprays
Pioneer Tara	Torch Shield	Steel Pick	Wears Gloves	Curly Blonde Hair	Water Sprays
Seeker Xena	Grappling Hook	Map Case	Bare Hands	Braided Red Hair	Water Sprays
Guardian Vera	Torch Shield	Signal Flare	Wears Gloves	Curly Blonde Hair	Water Sprays
Ranger Clara	Glider Pack	Brass Scope	Wears Gloves	Braided Red Hair	Bright Mirrors
Lookout Maya	Compass Ring	Rope Ladder	Wears Gloves	Braided Red Hair	Bright Mirrors
Hunter Hugo	Glider Pack	Signal Flare	Wears Gloves	Braided Red Hair	Water Sprays
Sentry Kara	Glider Pack	Map Case	Wears Gloves	Curly Blonde Hair	Water Sprays
Traveler Sam	Smoke Bomb	Steel Pick	Bare Hands	Braided Red Hair	Bright Mirrors
Scout Bruno	Grappling Hook	Steel Pick	Wears Gloves	Braided Red Hair	Water Sprays
Cadet Nico	Torch Shield	Steel Pick	Wears Gloves	Braided Red Hair	Bright Mirrors
Tracker Diego	Glider Pack	Signal Flare	Wears Gloves	Sleek Black Hair	Bright Mirrors
Pilot Iris	Grappling Hook	Rope Ladder	Bare Hands	Sleek Black Hair	Bright Mirrors
Rover Rosa	Grappling Hook	Brass Scope	Bare Hands	Sleek Black Hair	Loud Whistles
Sailor Finn	Glider Pack	Map Case	Wears Gloves	Braided Red Hair	Bright Mirrors
Officer Opal	Smoke Bomb	Brass Scope	Bare Hands	Sleek Black Hair	Water Sprays
Explorer Grace	Compass Ring	Map Case	Wears Gloves	Sleek Black Hair	Bright Mirrors

Clue 1

Pythagorean theorem

The island map shows a right triangle between two watchtowers and the vault entrance.

Solve each problem to learn its letter. Then write that letter in every box that shows the same number, and read the secret clue.

116

125

legs 60 and 63, hypotenuse =T

legs 8 and 15, hypotenuse =C

legs 24 and 70, hypotenuse =A

legs 25 and 60, hypotenuse =V

legs 40 and 42, hypotenuse =Y

legs 16 and 30, hypotenuse =I

legs 80 and 84, hypotenuse =N

legs 15 and 36, hypotenuse =D

legs 35 and 120, hypotenuse =R

legs 20 and 48, hypotenuse =S

legs 10 and 24, hypotenuse =P

legs 6 and 8, hypotenuse =O

legs 7 and 24, hypotenuse =H

legs 32 and 60, hypotenuse =E

legs 3 and 4, hypotenuse =L

legs 24 and 45, hypotenuse =M

0/16 letters found

Clue 2

Square roots

The ancient chamber floor is a large square laid out in equal tile rows.

Solve each problem to learn its letter. Then write that letter in every box that shows the same number, and read the secret clue.

sqrt(400) =G

sqrt(81) =H

sqrt(625) =U

sqrt(64) =L

sqrt(361) =V

sqrt(169) =I

sqrt(225) =N

sqrt(9) =F

sqrt(484) =P

sqrt(49) =R

sqrt(36) =O

sqrt(4) =T

sqrt(16) =S

sqrt(529) =E

sqrt(100) =W

sqrt(289) =D

sqrt(256) =A

0/17 letters found

Clue 3

Exponents

A glowing cave crystal multiplies its energy level during every hour of the night.

Solve each problem to learn its letter. Then write that letter in every box that shows the same number, and read the secret clue.

625

441

484

169

216

625

144

121

361

128

361

484

128

121

125

729

125

625

125

121

361

5^4 =B

3^6 =W

13^2 =M

11^2 =N

6^3 =O

3^3 =R

5^3 =A

21^2 =G

3^2 =U

2^5 =I

2^3 =T

19^2 =D

22^2 =H

6^2 =S

12^2 =L

2^2 =Y

2^7 =E

0/17 letters found

Clue 4

Order of operations

To solve the temple door mechanism, you must work through the symbols in order.

Solve each problem to learn its letter. Then write that letter in every box that shows the same number, and read the secret clue.

116

112

115

111

88 + 4 × 7 =B

63 + 3 × 8 =D

4 × 10 - 8 =L

47 + 8 × 8 =K

26 + 9 × 8 =W

11 × 10 - 11 =A

11 + 3 × 5 =O

11 × 12 - 20 =I

85 + 5 × 6 =C

12 × 4 - 2 =E

6 × 12 - 11 =R

3 × 7 - 11 =N

10 × 5 - 21 =P

7 + 5 × 3 =T

11 × 7 - 12 =H

6 × 12 - 22 =S

0/16 letters found

Clue 5

Square roots — the last clue

The secret escape hatch is a square metal plate with equal side lengths.

First solve each problem. Then find each answer in the list below and cross that sentence out. One sentence will be left — that's exactly what the villain did!

Step 1 — solve these

sqrt(36) = ?

sqrt(100) = ?

sqrt(121) = ?

sqrt(9) = ?

sqrt(144) = ?

sqrt(81) = ?

sqrt(25) = ?

sqrt(64) = ?

sqrt(4) = ?

sqrt(1) = ?

sqrt(49) = ?

Step 2 — cross out the sentence with each answer

1.The villain raised a torch shield, then adjusted a brass scope.

2.The villain flew a glider pack, then fired a signal flare.

3.The villain flew a glider pack, then chipped with a steel pick.

4.The villain flew a glider pack, then adjusted a brass scope.

5.The villain checked a compass ring, then opened a map case.

6.The villain checked a compass ring, then climbed a rope ladder.

7.The villain checked a compass ring, then adjusted a brass scope.

8.The villain flew a glider pack, then opened a map case.

9.The villain checked a compass ring, then fired a signal flare.

10.The villain raised a torch shield, then chipped with a steel pick.

11.The villain swung on a grappling hook, then adjusted a brass scope.

12.The villain threw a smoke bomb, then chipped with a steel pick.

Solve it

Name the culprit

Choose the one suspect left standing.

Answer Key — The Mystery of the Sunken Citadel

Culprit: Ranger Clara (Glider Pack · Brass Scope · Wears Gloves · Braided Red Hair · Bright Mirrors)

Clue 1 (Pythagorean theorem): "THE VILLAIN DOES NOT CARRY A MAP CASE"
legs 60 and 63, hypotenuse = 87 (T) · legs 8 and 15, hypotenuse = 17 (C) · legs 24 and 70, hypotenuse = 74 (A) · legs 25 and 60, hypotenuse = 65 (V) · legs 40 and 42, hypotenuse = 58 (Y) · legs 16 and 30, hypotenuse = 34 (I) · legs 80 and 84, hypotenuse = 116 (N) · legs 15 and 36, hypotenuse = 39 (D) · legs 35 and 120, hypotenuse = 125 (R) · legs 20 and 48, hypotenuse = 52 (S) · legs 10 and 24, hypotenuse = 26 (P) · legs 6 and 8, hypotenuse = 10 (O) · legs 7 and 24, hypotenuse = 25 (H) · legs 32 and 60, hypotenuse = 68 (E) · legs 3 and 4, hypotenuse = 5 (L) · legs 24 and 45, hypotenuse = 51 (M)
Clue 2 (Square roots): "GLOVED PRINTS WERE FOUND UPON THE VAULT"
sqrt(400) = 20 (G) · sqrt(81) = 9 (H) · sqrt(625) = 25 (U) · sqrt(64) = 8 (L) · sqrt(361) = 19 (V) · sqrt(169) = 13 (I) · sqrt(225) = 15 (N) · sqrt(9) = 3 (F) · sqrt(484) = 22 (P) · sqrt(49) = 7 (R) · sqrt(36) = 6 (O) · sqrt(4) = 2 (T) · sqrt(16) = 4 (S) · sqrt(529) = 23 (E) · sqrt(100) = 10 (W) · sqrt(289) = 17 (D) · sqrt(256) = 16 (A)
Clue 3 (Exponents): "BRIGHT MIRRORS BLINDED THE RUNAWAY BANDIT"
5^4 = 625 (B) · 3^6 = 729 (W) · 13^2 = 169 (M) · 11^2 = 121 (N) · 6^3 = 216 (O) · 3^3 = 27 (R) · 5^3 = 125 (A) · 21^2 = 441 (G) · 3^2 = 9 (U) · 2^5 = 32 (I) · 2^3 = 8 (T) · 19^2 = 361 (D) · 22^2 = 484 (H) · 6^2 = 36 (S) · 12^2 = 144 (L) · 2^2 = 4 (Y) · 2^7 = 128 (E)
Clue 4 (Order of operations): "BRAIDED RED HAIR WAS TRAPPED IN THE LOCK"
88 + 4 × 7 = 116 (B) · 63 + 3 × 8 = 87 (D) · 4 × 10 - 8 = 32 (L) · 47 + 8 × 8 = 111 (K) · 26 + 9 × 8 = 98 (W) · 11 × 10 - 11 = 99 (A) · 11 + 3 × 5 = 26 (O) · 11 × 12 - 20 = 112 (I) · 85 + 5 × 6 = 115 (C) · 12 × 4 - 2 = 46 (E) · 6 × 12 - 11 = 61 (R) · 3 × 7 - 11 = 10 (N) · 10 × 5 - 21 = 29 (P) · 7 + 5 × 3 = 22 (T) · 11 × 7 - 12 = 65 (H) · 6 × 12 - 22 = 50 (S)
Clue 5 (Square roots): surviving statement (box 4) → Ranger Clara
sqrt(36) = 6 · sqrt(100) = 10 · sqrt(121) = 11 · sqrt(9) = 3 · sqrt(144) = 12 · sqrt(81) = 9 · sqrt(25) = 5 · sqrt(64) = 8 · sqrt(4) = 2 · sqrt(1) = 1 · sqrt(49) = 7

About this mystery

Grade level: Grade 10 math
Math topics: Pythagorean theorem, Square roots, Exponents, Order of operations
Reading level: grades 3-4
Theme: The Mystery of the Sunken Citadel — set in Isla Mystica Ancient Ruins
Format: Interactive online & printable worksheet with answer key
Solution: One unique, verified culprit among 21 suspects

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