🚀 Space, MermaidsGrade 10Reading: grades 7-9Pythagorean theoremSquare rootsExponentsOrder of operations
The Cosmic Tide Caper
A rogue cosmic mermaid has disrupted the orbital deep-sea research station, sabotaging the flux core and escaping into the alien ocean trenches. The Starlight Guard needs your math skills to decode the sensor logs and unmask the culprit.
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 | Swim Propulsion | Star Gadget | Dominant Fin | Tail Glow | Sonar Frequency |
|---|---|---|---|---|---|
| Marina Sol | Hydro Jet | Nebula Net | Left Fin | Neon Cyan | Echo Pulse |
| Nerida Cross | Gravity Glide | Comet Laser | Right Fin | Solar Gold | Low Rumble |
| Cordelia Drift | Gravity Glide | Nebula Net | Left Fin | Deep Violet | High Pitch |
| Tycho Abyss | Hydro Jet | Solar Shield | Right Fin | Neon Cyan | Low Rumble |
| Callisto Wave | Plasma Tail | Void Prism | Right Fin | Deep Violet | Low Rumble |
| Orion Reef | Plasma Tail | Nebula Net | Right Fin | Solar Gold | High Pitch |
| Aquila Star | Gravity Glide | Solar Shield | Left Fin | Neon Cyan | Low Rumble |
| Corali Vance | Gravity Glide | Void Prism | Right Fin | Solar Gold | Low Rumble |
| Nixie Sterling | Plasma Tail | Solar Shield | Right Fin | Solar Gold | Low Rumble |
| Pearl Horizon | Hydro Jet | Stellar Beacon | Right Fin | Deep Violet | Low Rumble |
| Thalassa Moon | Gravity Glide | Comet Laser | Right Fin | Neon Cyan | Low Rumble |
| Triton Cole | Gravity Glide | Solar Shield | Left Fin | Solar Gold | Echo Pulse |
| Nereus Glen | Vortex Thruster | Solar Shield | Right Fin | Neon Cyan | Echo Pulse |
| Triton Sol | Plasma Tail | Nebula Net | Left Fin | Neon Cyan | High Pitch |
| Zephyr Currents | Quantum Fin | Solar Shield | Right Fin | Neon Cyan | Low Rumble |
| Hyperion Shell | Quantum Fin | Void Prism | Left Fin | Deep Violet | Low Rumble |
| Delphin Frost | Vortex Thruster | Void Prism | Left Fin | Deep Violet | High Pitch |
| Astra Kai | Vortex Thruster | Solar Shield | Right Fin | Neon Cyan | High Pitch |
| Calypso Ray | Hydro Jet | Void Prism | Left Fin | Solar Gold | Low Rumble |
| Marina Drake | Plasma Tail | Void Prism | Right Fin | Neon Cyan | Low Rumble |
| Cassiopeia Wave | Vortex Thruster | Void Prism | Right Fin | Neon Cyan | Low Rumble |
Clue 1
Pythagorean theorem
The navigation sensor calculates direct distance across the ocean trench coordinates.
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
123
26
20
65
75
51
51
34
75
58
85
52
20
25
58
52
T
123
111
25
20
34
82
52
68
20
T
123
51
34
25
20
100
legs 27 and 120, hypotenuse =T
legs 12 and 16, hypotenuse =E
legs 36 and 105, hypotenuse =U
legs 24 and 45, hypotenuse =L
legs 40 and 75, hypotenuse =D
legs 32 and 60, hypotenuse =M
legs 16 and 30, hypotenuse =A
legs 10 and 24, hypotenuse =H
legs 18 and 80, hypotenuse =C
legs 25 and 60, hypotenuse =V
legs 28 and 96, hypotenuse =R
legs 20 and 48, hypotenuse =O
legs 15 and 20, hypotenuse =S
legs 21 and 72, hypotenuse =I
legs 40 and 42, hypotenuse =N
0/15 letters found
Clue 2
Square roots
Analyzing the surface area of the bio energy shield reveals its base signal radius.
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
10
5
8
7
23
7
19
8
15
T
10
23
7
8
7
T
10
5
8
9
11
11
9
17
5
T
10
24
9
13
T
10
25
7
T
10
8
8
11
sqrt(100) =T
sqrt(64) =E
sqrt(49) =S
sqrt(121) =R
sqrt(529) =U
sqrt(289) =G
sqrt(25) =H
sqrt(225) =C
sqrt(625) =O
sqrt(361) =P
sqrt(169) =N
sqrt(576) =F
sqrt(81) =I
0/13 letters found
Clue 3
Exponents
Measuring the exponential growth of stellar energy in the hydro core gives a clue.
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
512
400
25
196
441
196
243
25
9
T
512
256
36
196
196
T
512
8
243
243
25
729
121
128
36
125
8
256
216
441
484
121
125
25
8^3 =T
5^2 =E
6^2 =A
2^3 =O
22^2 =M
2^7 =Y
11^2 =B
5^3 =L
2^8 =W
3^5 =P
3^2 =C
21^2 =U
14^2 =S
9^3 =D
20^2 =H
6^3 =R
0/16 letters found
Clue 4
Order of operations
Decoding the sequence of operational commands from the submarine log pinpoints the next location.
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
52
35
61
11
117
11
95
61
7
T
52
11
35
61
30
11
17
46
61
65
46
7
76
17
46
11
35
18
46
61
11 × 5 - 3 =T
30 + 5 × 7 =O
6 × 2 - 5 =C
79 + 4 × 4 =P
17 + 6 × 3 =H
3 × 7 - 4 =A
12 × 11 - 15 =U
4 × 7 - 10 =I
37 + 6 × 4 =E
9 × 11 - 23 =Y
11 × 3 - 3 =D
22 + 3 × 8 =N
3 × 6 - 7 =S
0/13 letters found
Clue 5
Square roots — the last clue
Calculating the root frequency of the localized sonar wave isolates the rogue profile.
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(25) = ?
sqrt(1) = ?
sqrt(100) = ?
sqrt(121) = ?
sqrt(9) = ?
sqrt(64) = ?
sqrt(4) = ?
sqrt(49) = ?
sqrt(81) = ?
sqrt(144) = ?
sqrt(16) = ?
Step 2 — cross out the sentence with each answer
1.The villain blasted past the reef with hydro jets, then deflected laser fire behind a solar shield.
2.The villain drifted on currents via gravity glide, then cut through the hull with a comet laser.
3.The villain shot through tides with vortex thrusters, then lit up the trench using a stellar beacon.
4.The villain shot through tides with vortex thrusters, then cut through the hull with a comet laser.
5.The villain shot through tides with vortex thrusters, then trapped the patrol using a void prism.
6.The villain warped through water using a plasma tail, then trapped the patrol using a void prism.
7.The villain warped through water using a plasma tail, then snared the research pod in a nebula net.
8.The villain drifted on currents via gravity glide, then lit up the trench using a stellar beacon.
9.The villain warped through water using a plasma tail, then lit up the trench using a stellar beacon.
10.The villain surged through the deep with a quantum fin, then deflected laser fire behind a solar shield.
11.The villain drifted on currents via gravity glide, then snared the research pod in a nebula net.
12.The villain blasted past the reef with hydro jets, then trapped the patrol using a void prism.
Solve it
Name the culprit
Choose the one suspect left standing.
Answer Key — The Cosmic Tide Caper
Culprit: Marina Drake (Plasma Tail · Void Prism · Right Fin · Neon Cyan · Low Rumble)
- Clue 1 (Pythagorean theorem): "THE VILLAIN DOES NOT USE A COMET LASER"legs 27 and 120, hypotenuse = 123 (T) · legs 12 and 16, hypotenuse = 20 (E) · legs 36 and 105, hypotenuse = 111 (U) · legs 24 and 45, hypotenuse = 51 (L) · legs 40 and 75, hypotenuse = 85 (D) · legs 32 and 60, hypotenuse = 68 (M) · legs 16 and 30, hypotenuse = 34 (A) · legs 10 and 24, hypotenuse = 26 (H) · legs 18 and 80, hypotenuse = 82 (C) · legs 25 and 60, hypotenuse = 65 (V) · legs 28 and 96, hypotenuse = 100 (R) · legs 20 and 48, hypotenuse = 52 (O) · legs 15 and 20, hypotenuse = 25 (S) · legs 21 and 72, hypotenuse = 75 (I) · legs 40 and 42, hypotenuse = 58 (N)
- Clue 2 (Square roots): "THE SUSPECT USES THEIR RIGHT FIN TO STEER"sqrt(100) = 10 (T) · sqrt(64) = 8 (E) · sqrt(49) = 7 (S) · sqrt(121) = 11 (R) · sqrt(529) = 23 (U) · sqrt(289) = 17 (G) · sqrt(25) = 5 (H) · sqrt(225) = 15 (C) · sqrt(625) = 25 (O) · sqrt(361) = 19 (P) · sqrt(169) = 13 (N) · sqrt(576) = 24 (F) · sqrt(81) = 9 (I)
- Clue 3 (Exponents): "THE SUSPECT WAS STOPPED BY A LOW RUMBLE"8^3 = 512 (T) · 5^2 = 25 (E) · 6^2 = 36 (A) · 2^3 = 8 (O) · 22^2 = 484 (M) · 2^7 = 128 (Y) · 11^2 = 121 (B) · 5^3 = 125 (L) · 2^8 = 256 (W) · 3^5 = 243 (P) · 3^2 = 9 (C) · 21^2 = 441 (U) · 14^2 = 196 (S) · 9^3 = 729 (D) · 20^2 = 400 (H) · 6^3 = 216 (R)
- Clue 4 (Order of operations): "THE SUSPECT SHEDS A NEON CYAN SHINE"11 × 5 - 3 = 52 (T) · 30 + 5 × 7 = 65 (O) · 6 × 2 - 5 = 7 (C) · 79 + 4 × 4 = 95 (P) · 17 + 6 × 3 = 35 (H) · 3 × 7 - 4 = 17 (A) · 12 × 11 - 15 = 117 (U) · 4 × 7 - 10 = 18 (I) · 37 + 6 × 4 = 61 (E) · 9 × 11 - 23 = 76 (Y) · 11 × 3 - 3 = 30 (D) · 22 + 3 × 8 = 46 (N) · 3 × 6 - 7 = 11 (S)
- Clue 5 (Square roots): surviving statement (box 6) → Marina Drakesqrt(25) = 5 · sqrt(1) = 1 · sqrt(100) = 10 · sqrt(121) = 11 · sqrt(9) = 3 · sqrt(64) = 8 · sqrt(4) = 2 · sqrt(49) = 7 · sqrt(81) = 9 · sqrt(144) = 12 · 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 Cosmic Tide Caper — set in Aqua-Centauri Prime, an ocean world orbiting a distant twin star system
- Format
- Interactive online & printable worksheet with answer key
- Solution
- One unique, verified culprit among 21 suspects