Grade 10Reading: grades 7-9Pythagorean theoremSquare rootsExponentsOrder of operations

The Case of the Missing Cloud Crystal

During the annual Sky Citadel Regatta, someone sabotaged the main power grid and pinched the hyper-crystal powering the flagship. You must examine the flight logs and physical evidence left at the hangar bay to narrow down the suspects before the culprit escapes into the slipstream.

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	Airship Gear	Gadget	Glove Hand	Goggle Strap Color	Tricked By
Pilot Clara	Magnetic Boots	Smoke Canister	Left Handed	Copper Strap	Net Trap
Stoker Oscar	Brass Compass	Thermal Scanner	Left Handed	Leather Strap	Net Trap
Spotter Willa	Steam Jetpack	Signal Whistle	Left Handed	Copper Strap	Net Trap
Officer Greta	Glider Wings	Signal Whistle	Left Handed	Leather Strap	Whistle Blast
Scout Elena	Brass Compass	Smoke Canister	Left Handed	Copper Strap	Net Trap
Tracker Yael	Glider Wings	Signal Whistle	Left Handed	Leather Strap	Net Trap
Sailor Stella	Grapple Launcher	Decoy Flare	Right Handed	Silver Strap	Mirror Reflection
Signalman Maya	Glider Wings	Flash Beacon	Right Handed	Silver Strap	Whistle Blast
Quartermaster Cora	Brass Compass	Smoke Canister	Right Handed	Silver Strap	Net Trap
Mechanic Felix	Grapple Launcher	Signal Whistle	Right Handed	Leather Strap	Net Trap
Cadet Quinn	Steam Jetpack	Smoke Canister	Right Handed	Silver Strap	Whistle Blast
Archer Reed	Grapple Launcher	Signal Whistle	Right Handed	Copper Strap	Net Trap
Rigging Iris	Steam Jetpack	Smoke Canister	Left Handed	Copper Strap	Net Trap
Scholar Una	Magnetic Boots	Thermal Scanner	Left Handed	Leather Strap	Whistle Blast
Vanguard Vance	Steam Jetpack	Signal Whistle	Left Handed	Leather Strap	Net Trap
Helmsman Jasper	Brass Compass	Signal Whistle	Left Handed	Leather Strap	Mirror Reflection
Engineer Drake	Grapple Launcher	Signal Whistle	Left Handed	Silver Strap	Net Trap
Rigger Leo	Glider Wings	Thermal Scanner	Left Handed	Copper Strap	Net Trap
Lookout Piper	Grapple Launcher	Smoke Canister	Left Handed	Leather Strap	Net Trap
Captain Avery	Glider Wings	Smoke Canister	Right Handed	Copper Strap	Mirror Reflection
Tinker Theo	Brass Compass	Decoy Flare	Left Handed	Leather Strap	Net Trap

Clue 1

Pythagorean theorem

You plot the airship flight path on a grid to find the diagonal distance between the hangar towers.

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

123

116

legs 24 and 70, hypotenuse =T

legs 10 and 24, hypotenuse =H

legs 21 and 72, hypotenuse =N

legs 18 and 24, hypotenuse =O

legs 80 and 84, hypotenuse =E

legs 60 and 63, hypotenuse =Y

legs 6 and 8, hypotenuse =S

legs 12 and 16, hypotenuse =P

legs 24 and 32, hypotenuse =R

legs 15 and 36, hypotenuse =L

legs 27 and 120, hypotenuse =F

legs 18 and 80, hypotenuse =A

legs 24 and 45, hypotenuse =U

legs 9 and 12, hypotenuse =D

legs 3 and 4, hypotenuse =C

0/15 letters found

Clue 2

Square roots

To unlock the deck vault, you must find the side length of the square landing pad.

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(49) =T

sqrt(25) =S

sqrt(289) =E

sqrt(400) =L

sqrt(529) =U

sqrt(121) =I

sqrt(196) =O

sqrt(36) =D

sqrt(576) =A

sqrt(169) =H

sqrt(484) =N

sqrt(16) =F

sqrt(4) =V

sqrt(256) =R

0/14 letters found

Clue 3

Exponents

The pressure sensor logs reveal energy output rising by powers of two during the breach.

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

441

289

441

729

343

216

484

441

343

484

289

324

169

144

484

225

512

144

196

484

729

2^2 =T

22^2 =A

3^4 =E

21^2 =S

13^2 =I

8^3 =Y

15^2 =V

18^2 =G

6^3 =W

7^3 =C

14^2 =R

3^6 =P

7^2 =H

17^2 =U

12^2 =N

0/15 letters found

Clue 4

Order of operations

Decoding the vault logs requires evaluating the multi-step security sequence.

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

118

101

8 × 4 - 3 =T

7 × 12 - 27 =E

25 + 3 × 6 =U

5 × 7 - 4 =S

4 + 9 × 8 =G

11 + 4 × 2 =H

74 + 9 × 3 =P

12 × 4 - 24 =A

55 + 7 × 9 =C

11 + 2 × 7 =M

3 + 6 × 2 =F

22 + 8 × 2 =O

4 × 6 - 16 =I

11 × 6 - 6 =L

6 × 10 - 25 =R

9 + 2 × 2 =V

14 + 7 × 6 =D

34 + 7 × 4 =N

0/18 letters found

Clue 5

Square roots — the last clue

Measuring the area of the stolen crystal room gives the side dimension of its square base.

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(121) = ?

sqrt(1) = ?

sqrt(9) = ?

sqrt(4) = ?

sqrt(25) = ?

sqrt(49) = ?

sqrt(144) = ?

sqrt(64) = ?

sqrt(81) = ?

sqrt(16) = ?

Step 2 — cross out the sentence with each answer

1.The villain deployed glider wings, then signaled allies with a whistle.

2.The villain checked a brass compass, then blinded guards with a flash beacon.

3.The villain blasted a steam jetpack, then blinded guards with a flash beacon.

4.The villain marched with magnetic boots, then blinded guards with a flash beacon.

5.The villain checked a brass compass, then signaled allies with a whistle.

6.The villain fired a grapple launcher, then vanished behind a smoke canister.

7.The villain fired a grapple launcher, then signaled allies with a whistle.

8.The villain marched with magnetic boots, then vanished behind a smoke canister.

9.The villain deployed glider wings, then blinded guards with a flash beacon.

10.The villain checked a brass compass, then tracked targets with a thermal scanner.

11.The villain blasted a steam jetpack, then signaled allies with a whistle.

12.The villain blasted a steam jetpack, then tracked targets with a thermal scanner.

Solve it

Name the culprit

Choose the one suspect left standing.

Answer Key — The Case of the Missing Cloud Crystal

Culprit: Stoker Oscar (Brass Compass · Thermal Scanner · Left Handed · Leather Strap · Net Trap)

Clue 1 (Pythagorean theorem): "THE SUSPECT DOES NOT USE A DECOY FLARE"
legs 24 and 70, hypotenuse = 74 (T) · legs 10 and 24, hypotenuse = 26 (H) · legs 21 and 72, hypotenuse = 75 (N) · legs 18 and 24, hypotenuse = 30 (O) · legs 80 and 84, hypotenuse = 116 (E) · legs 60 and 63, hypotenuse = 87 (Y) · legs 6 and 8, hypotenuse = 10 (S) · legs 12 and 16, hypotenuse = 20 (P) · legs 24 and 32, hypotenuse = 40 (R) · legs 15 and 36, hypotenuse = 39 (L) · legs 27 and 120, hypotenuse = 123 (F) · legs 18 and 80, hypotenuse = 82 (A) · legs 24 and 45, hypotenuse = 51 (U) · legs 9 and 12, hypotenuse = 15 (D) · legs 3 and 4, hypotenuse = 5 (C)
Clue 2 (Square roots): "THE VILLAIN USED THEIR LEFT HAND ON THE LEVER"
sqrt(49) = 7 (T) · sqrt(25) = 5 (S) · sqrt(289) = 17 (E) · sqrt(400) = 20 (L) · sqrt(529) = 23 (U) · sqrt(121) = 11 (I) · sqrt(196) = 14 (O) · sqrt(36) = 6 (D) · sqrt(576) = 24 (A) · sqrt(169) = 13 (H) · sqrt(484) = 22 (N) · sqrt(16) = 4 (F) · sqrt(4) = 2 (V) · sqrt(256) = 16 (R)
Clue 3 (Exponents): "THE SUSPECT WAS CAUGHT IN A HEAVY NET TRAP"
2^2 = 4 (T) · 22^2 = 484 (A) · 3^4 = 81 (E) · 21^2 = 441 (S) · 13^2 = 169 (I) · 8^3 = 512 (Y) · 15^2 = 225 (V) · 18^2 = 324 (G) · 6^3 = 216 (W) · 7^3 = 343 (C) · 14^2 = 196 (R) · 3^6 = 729 (P) · 7^2 = 49 (H) · 17^2 = 289 (U) · 12^2 = 144 (N)
Clue 4 (Order of operations): "THE DETECTIVE FOUND A LEATHER STRAP FRAGMENT"
8 × 4 - 3 = 29 (T) · 7 × 12 - 27 = 57 (E) · 25 + 3 × 6 = 43 (U) · 5 × 7 - 4 = 31 (S) · 4 + 9 × 8 = 76 (G) · 11 + 4 × 2 = 19 (H) · 74 + 9 × 3 = 101 (P) · 12 × 4 - 24 = 24 (A) · 55 + 7 × 9 = 118 (C) · 11 + 2 × 7 = 25 (M) · 3 + 6 × 2 = 15 (F) · 22 + 8 × 2 = 38 (O) · 4 × 6 - 16 = 8 (I) · 11 × 6 - 6 = 60 (L) · 6 × 10 - 25 = 35 (R) · 9 + 2 × 2 = 13 (V) · 14 + 7 × 6 = 56 (D) · 34 + 7 × 4 = 62 (N)
Clue 5 (Square roots): surviving statement (box 10) → Stoker Oscar
sqrt(36) = 6 · sqrt(121) = 11 · sqrt(1) = 1 · sqrt(9) = 3 · sqrt(4) = 2 · sqrt(25) = 5 · sqrt(49) = 7 · sqrt(144) = 12 · sqrt(64) = 8 · sqrt(81) = 9 · sqrt(16) = 4

About this mystery

Grade level: Grade 10 math
Math topics: Pythagorean theorem, Square roots, Exponents, Order of operations
Reading level: grades 7-9
Theme: The Case of the Missing Cloud Crystal — set in The Floating Citadel of Aethelgard
Format: Interactive online & printable worksheet with answer key
Solution: One unique, verified culprit among 21 suspects

More free printable math cases

10th grade worksheets Exponents worksheets Order of operations worksheets Square roots worksheets Pythagorean theorem worksheets All worksheets →

The Mystery of the Cloud Fortress

Grade 10

The Sunstone Temple Heist

Grade 10

The Mystery of the Skyward Compass

Grade 10

The Case of the Missing Championship Basketball

Grade 10