Grade 10Reading: grades 7-9Pythagorean theoremWord problemsSquare rootsExponents
The Mystery of the Cloud Fortress
Someone sabotaged the Sky Citadel's main compass during the annual cloud festival! The Master Navigator needs your detective skills to analyze field notes, calculate flight distances, and identify the culprit before they escape into the upper atmosphere.
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 Tool | Glider Type | Dominant Hand | Goggle Color | Fears |
|---|---|---|---|---|---|
| Beatrice Cloud | Steam Cannon | Jet Parasol | Left Handed | Amber Lenses | High Gusts |
| Amelia Airhart | Sonic Whistle | Jet Parasol | Right Handed | Emerald Lenses | Bright Flash |
| Nova Breeze | Steam Cannon | Box Kite | Right Handed | Amber Lenses | Bright Flash |
| Oswald Cirrus | Pulse Lantern | Delta Wing | Left Handed | Amber Lenses | High Gusts |
| Silas Drake | Sonic Whistle | Solar Wings | Right Handed | Amber Lenses | High Gusts |
| Rosalind Horizon | Steam Cannon | Solar Wings | Right Handed | Emerald Lenses | High Gusts |
| Quinn Nimbus | Sonic Whistle | Delta Wing | Left Handed | Amber Lenses | Loud Thunder |
| Mara Sterling | Wind Banner | Jet Parasol | Left Handed | Amber Lenses | Loud Thunder |
| Felix Gale | Brass Grapple | Delta Wing | Right Handed | Amber Lenses | High Gusts |
| Lyra Falcon | Steam Cannon | Bat Glider | Right Handed | Cobalt Lenses | High Gusts |
| Eliza Windham | Wind Banner | Jet Parasol | Right Handed | Amber Lenses | High Gusts |
| Ignatius Skye | Wind Banner | Box Kite | Right Handed | Amber Lenses | High Gusts |
| Penelope Vane | Brass Grapple | Solar Wings | Left Handed | Amber Lenses | Loud Thunder |
| Gideon Frost | Steam Cannon | Box Kite | Left Handed | Emerald Lenses | High Gusts |
| Corbin Sterling | Steam Cannon | Solar Wings | Right Handed | Amber Lenses | Bright Flash |
| Jasper Vance | Wind Banner | Delta Wing | Left Handed | Amber Lenses | Bright Flash |
| Zephyr Finch | Brass Grapple | Box Kite | Right Handed | Cobalt Lenses | Loud Thunder |
| Thaddeus Soar | Sonic Whistle | Box Kite | Right Handed | Amber Lenses | High Gusts |
| Juliet Ridge | Wind Banner | Solar Wings | Right Handed | Emerald Lenses | High Gusts |
| Vesper Wing | Brass Grapple | Box Kite | Right Handed | Amber Lenses | High Gusts |
| Magnus Zenith | Wind Banner | Bat Glider | Right Handed | Amber Lenses | High Gusts |
Clue 1
Pythagorean theorem
You review the logbook entries recording supply distribution before the sabotage to track the suspect's movements.
Solve each problem to learn its letter. Then write that letter in every box that shows the same number, and read the secret clue.
T
58
74
37
51
39
51
100
37
68
T
58
13
116
37
51
87
116
T
58
39
51
37
111
15
116
29
41
52
T
58
37
legs 40 and 42, hypotenuse =T
legs 20 and 21, hypotenuse =X
legs 9 and 40, hypotenuse =K
legs 5 and 12, hypotenuse =D
legs 9 and 12, hypotenuse =B
legs 24 and 70, hypotenuse =H
legs 24 and 45, hypotenuse =S
legs 60 and 63, hypotenuse =N
legs 28 and 96, hypotenuse =P
legs 15 and 36, hypotenuse =U
legs 80 and 84, hypotenuse =O
legs 32 and 60, hypotenuse =C
legs 36 and 105, hypotenuse =A
legs 12 and 35, hypotenuse =E
legs 20 and 48, hypotenuse =I
0/15 letters found
Clue 2
Word problems
To pinpoint where the pirate launched, calculate the hypotenuse between the fortress watchtowers and the airship deck.
Solve each problem to learn its letter, then write the letters in the boxes to fill in the missing word.
Awitnesssawthevillainwas .
R
11
33
104
74
29
74
31
50
D
E
D
Sky scout found 3 spyglasses yesterday and 8 more today. How many spyglasses in all?R
There were 89 brass gears. 39 were used up. How many brass gears are left?N
There were 142 spyglasses. 38 were used up. How many spyglasses are left?G
Sky scout found 14 brass gears yesterday and 60 more today. How many brass gears in all?H
There were 68 signal flares. 39 were used up. How many signal flares are left?T
Sky scout found 7 spyglasses yesterday and 24 more today. How many spyglasses in all?A
There were 36 compasses. 3 were used up. How many compasses are left?I
0/7 letters found
Clue 3
Square roots
Analyzing the area of the damaged hull grid reveals an exact square, leading to a crucial root value.
Solve each problem to learn its letter. Then write that letter in every box that shows the same number, and read the secret clue.
T
11
6
10
25
17
21
8
10
9
13
10
12
19
6
10
14
6
7
T
11
22
3
6
7
21
6
21
8
16
T
11
16
sqrt(121) =T
sqrt(169) =L
sqrt(196) =N
sqrt(81) =F
sqrt(441) =G
sqrt(484) =B
sqrt(144) =D
sqrt(49) =I
sqrt(36) =H
sqrt(64) =U
sqrt(9) =Y
sqrt(361) =W
sqrt(289) =O
sqrt(256) =S
sqrt(100) =E
sqrt(625) =R
0/16 letters found
Clue 4
Exponents
The rogue's power source surged exponentially during the escape, requiring exponential equations to decode the energy signature.
Solve each problem to learn its letter. Then write that letter in every box that shows the same number, and read the secret clue.
W
289
216
484
225
243
512
512
243
512
512
32
W
289
16
243
64
8
243
256
484
216
27
225
512
216
225
32
9
400
243
16
8
243
225
512
243
512
17^2 =W
20^2 =B
8^3 =S
22^2 =T
6^3 =I
2^3 =L
2^4 =R
4^3 =F
3^2 =M
2^8 =C
15^2 =N
2^5 =A
3^3 =O
3^5 =E
0/14 letters found
Clue 5
Square roots — the last clue
A second grid of flight trajectory coordinates forms another perfect square that yields the final hidden coordinate root.
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(1) = ?
sqrt(25) = ?
sqrt(16) = ?
sqrt(49) = ?
sqrt(121) = ?
sqrt(144) = ?
sqrt(100) = ?
sqrt(9) = ?
sqrt(4) = ?
sqrt(64) = ?
sqrt(81) = ?
Step 2 — cross out the sentence with each answer
1.The villain disrupted signals with a sonic whistle, then escaped on solar wings.
2.The villain blasted the vault door with a steam cannon, then floated down on a box kite.
3.The villain disrupted signals with a sonic whistle, then floated down on a box kite.
4.The villain swung in using a brass grapple, then glided off with a delta wing.
5.The villain signaled the crew with a wind banner, then vanished under a jet parasol.
6.The villain signaled the crew with a wind banner, then soared away using a bat glider.
7.The villain swung in using a brass grapple, then vanished under a jet parasol.
8.The villain signaled the crew with a wind banner, then escaped on solar wings.
9.The villain blasted the vault door with a steam cannon, then vanished under a jet parasol.
10.The villain blinded guards with a pulse lantern, then soared away using a bat glider.
11.The villain blinded guards with a pulse lantern, then glided off with a delta wing.
12.The villain blinded guards with a pulse lantern, then escaped on solar wings.
Solve it
Name the culprit
Choose the one suspect left standing.
Answer Key — The Mystery of the Cloud Fortress
Culprit: Magnus Zenith (Wind Banner · Bat Glider · Right Handed · Amber Lenses · High Gusts)
- Clue 1 (Pythagorean theorem): "THE SUSPECT DOES NOT USE A BOX KITE"legs 40 and 42, hypotenuse = 58 (T) · legs 20 and 21, hypotenuse = 29 (X) · legs 9 and 40, hypotenuse = 41 (K) · legs 5 and 12, hypotenuse = 13 (D) · legs 9 and 12, hypotenuse = 15 (B) · legs 24 and 70, hypotenuse = 74 (H) · legs 24 and 45, hypotenuse = 51 (S) · legs 60 and 63, hypotenuse = 87 (N) · legs 28 and 96, hypotenuse = 100 (P) · legs 15 and 36, hypotenuse = 39 (U) · legs 80 and 84, hypotenuse = 116 (O) · legs 32 and 60, hypotenuse = 68 (C) · legs 36 and 105, hypotenuse = 111 (A) · legs 12 and 35, hypotenuse = 37 (E) · legs 20 and 48, hypotenuse = 52 (I)
- Clue 2 (Word problems): "RIGHT HANDED"Sky scout found 3 spyglasses yesterday and 8 more today. How many spyglasses in all? = 11 (R) · There were 89 brass gears. 39 were used up. How many brass gears are left? = 50 (N) · There were 142 spyglasses. 38 were used up. How many spyglasses are left? = 104 (G) · Sky scout found 14 brass gears yesterday and 60 more today. How many brass gears in all? = 74 (H) · There were 68 signal flares. 39 were used up. How many signal flares are left? = 29 (T) · Sky scout found 7 spyglasses yesterday and 24 more today. How many spyglasses in all? = 31 (A) · There were 36 compasses. 3 were used up. How many compasses are left? = 33 (I)
- Clue 3 (Square roots): "THE ROGUE FLED WHEN HIT BY HIGH GUSTS"sqrt(121) = 11 (T) · sqrt(169) = 13 (L) · sqrt(196) = 14 (N) · sqrt(81) = 9 (F) · sqrt(441) = 21 (G) · sqrt(484) = 22 (B) · sqrt(144) = 12 (D) · sqrt(49) = 7 (I) · sqrt(36) = 6 (H) · sqrt(64) = 8 (U) · sqrt(9) = 3 (Y) · sqrt(361) = 19 (W) · sqrt(289) = 17 (O) · sqrt(256) = 16 (S) · sqrt(100) = 10 (E) · sqrt(625) = 25 (R)
- Clue 4 (Exponents): "WITNESSES SAW REFLECTIONS IN AMBER LENSES"17^2 = 289 (W) · 20^2 = 400 (B) · 8^3 = 512 (S) · 22^2 = 484 (T) · 6^3 = 216 (I) · 2^3 = 8 (L) · 2^4 = 16 (R) · 4^3 = 64 (F) · 3^2 = 9 (M) · 2^8 = 256 (C) · 15^2 = 225 (N) · 2^5 = 32 (A) · 3^3 = 27 (O) · 3^5 = 243 (E)
- Clue 5 (Square roots): surviving statement (box 6) → Magnus Zenithsqrt(1) = 1 · sqrt(25) = 5 · sqrt(16) = 4 · sqrt(49) = 7 · sqrt(121) = 11 · sqrt(144) = 12 · sqrt(100) = 10 · sqrt(9) = 3 · sqrt(4) = 2 · sqrt(64) = 8 · sqrt(81) = 9
About this mystery
- Grade level
- Grade 10 math
- Math topics
- Pythagorean theorem, Word problems, Square roots, Exponents
- Reading level
- grades 7-9
- Theme
- The Mystery of the Cloud Fortress — set in Sky Citadel Aerie
- Format
- Interactive online & printable worksheet with answer key
- Solution
- One unique, verified culprit among 21 suspects