Grade 8Reading: grades 7-9ExponentsSquare rootsPythagorean theoremOrder of operationsTwo-step equations
The Mystery of the Abyss Engine
A rogue diver sabotaged the submarine main generator and hid the emergency power core in the deep trenches. Decipher the telemetry logs to 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 | Diving Tech | Gadget | Dominant Hand | Wetsuit Hood | Phobia |
|---|---|---|---|---|---|
| Leo Sterling | Thermal Suit | Signal Jammer | Right Handed | Cobalt Blue Hood | High Pitch Tones |
| Marcus Vance | Deep Radar | Flash Grenade | Right Handed | Crimson Red Hood | High Pitch Tones |
| Nadia Ray | Thermal Suit | Smoke Canister | Right Handed | Cobalt Blue Hood | Bright Lights |
| Iris Mercer | Plasma Cutter | Flash Grenade | Right Handed | Cobalt Blue Hood | Bright Lights |
| Captain Drake | Plasma Cutter | Flash Grenade | Left Handed | Crimson Red Hood | Bright Lights |
| Commander Holt | Thermal Suit | Signal Jammer | Right Handed | Crimson Red Hood | Magnetic Fields |
| Dr Aris Thorne | Hydro Thrusters | Signal Jammer | Right Handed | Cobalt Blue Hood | Magnetic Fields |
| Owen Vance | Hydro Thrusters | Signal Jammer | Left Handed | Crimson Red Hood | Magnetic Fields |
| Olivia Chen | Thermal Suit | Grappling Hook | Right Handed | Crimson Red Hood | High Pitch Tones |
| Kai Rivera | Deep Radar | Signal Jammer | Right Handed | Crimson Red Hood | Magnetic Fields |
| Jax Brooks | Deep Radar | Signal Jammer | Left Handed | Neon Yellow Hood | Bright Lights |
| Samuel Bishop | Sonar Pulse | Laser Pointer | Right Handed | Crimson Red Hood | Magnetic Fields |
| Elena Cruz | Plasma Cutter | Grappling Hook | Right Handed | Crimson Red Hood | High Pitch Tones |
| Cora West | Plasma Cutter | Grappling Hook | Right Handed | Crimson Red Hood | Magnetic Fields |
| Professor Finch | Sonar Pulse | Flash Grenade | Left Handed | Crimson Red Hood | Magnetic Fields |
| Hugo Frost | Plasma Cutter | Laser Pointer | Right Handed | Neon Yellow Hood | Magnetic Fields |
| Zoe Gallagher | Thermal Suit | Flash Grenade | Right Handed | Neon Yellow Hood | Bright Lights |
| Nina Petrov | Hydro Thrusters | Grappling Hook | Right Handed | Crimson Red Hood | High Pitch Tones |
| Tessa Rhodes | Thermal Suit | Signal Jammer | Left Handed | Crimson Red Hood | Bright Lights |
| Silas Kane | Sonar Pulse | Signal Jammer | Right Handed | Crimson Red Hood | Magnetic Fields |
| Victor Vance | Thermal Suit | Flash Grenade | Left Handed | Cobalt Blue Hood | Bright Lights |
Clue 1
Exponents
The diving computer encrypted the generator status logs into exponential scales. Calculate the values to decode the first 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
289
25
100
324
36
243
243
4
36
625
144
16
100
400
625
16
T
289
32
400
100
4
243
4
400
100
361
729
16
36
625
T
289
100
361
17^2 =T
9^3 =P
6^2 =I
12^2 =D
2^5 =U
2^4 =O
2^2 =A
19^2 =R
18^2 =V
3^5 =L
20^2 =S
10^2 =E
5^4 =N
5^2 =H
0/14 letters found
Clue 2
Square roots
To map out the exact square bay where the thief fled, calculate the square roots of these area measurements.
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
17
16
18
14
13
14
19
18
15
T
17
2
14
25
2
5
16
T
17
16
10
7
22
18
22
sqrt(289) =T
sqrt(25) =G
sqrt(324) =E
sqrt(625) =R
sqrt(169) =U
sqrt(4) =I
sqrt(100) =A
sqrt(256) =H
sqrt(225) =C
sqrt(49) =N
sqrt(484) =D
sqrt(196) =S
sqrt(361) =P
0/13 letters found
Clue 3
Pythagorean theorem
The sub navigator tracked the diagonal escape path across the docking grid. Use the Pythagorean theorem to calculate the distance.
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
34
17
37
58
41
82
82
74
41
68
26
87
37
74
5
68
37
26
26
41
26
25
74
39
68
37
T
34
41
13
52
41
37
82
51
26
legs 16 and 30, hypotenuse =T
legs 3 and 4, hypotenuse =K
legs 24 and 70, hypotenuse =A
legs 20 and 48, hypotenuse =F
legs 18 and 80, hypotenuse =L
legs 32 and 60, hypotenuse =N
legs 15 and 36, hypotenuse =G
legs 10 and 24, hypotenuse =S
legs 15 and 20, hypotenuse =M
legs 40 and 42, hypotenuse =V
legs 60 and 63, hypotenuse =W
legs 24 and 45, hypotenuse =D
legs 5 and 12, hypotenuse =C
legs 8 and 15, hypotenuse =H
legs 9 and 40, hypotenuse =I
legs 12 and 35, hypotenuse =E
0/16 letters found
Clue 4
Order of operations
To unlock the emergency terminal, solve the order of operations code sequence programmed on the keypad.
Solve each problem to learn its letter. Then write that letter in every box that shows the same number, and read the secret clue.
A
54
45
19
25
11
47
32
90
19
53
46
36
32
32
46
87
A
54
47
47
53
53
90
32
90
45
A
54
11
53
19
A
54
5 × 11 - 1 =A
10 × 7 - 24 =D
10 × 6 - 13 =S
4 × 12 - 12 =H
3 × 9 - 2 =I
11 × 9 - 9 =N
8 × 9 - 27 =C
7 × 2 - 3 =M
8 × 11 - 1 =W
3 × 7 - 2 =R
11 × 3 - 1 =O
8 + 9 × 5 =E
0/12 letters found
Clue 5
Two-step equations — the last clue
The base engineer set up balanced algebraic equations to uncover the final hidden pressure reading.
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
4x + 11 = 23, x = ?
3x + 3 = 15, x = ?
3x + 1 = 34, x = ?
4x + 6 = 26, x = ?
5x + 1 = 36, x = ?
3x + 1 = 4, x = ?
4x + 11 = 51, x = ?
2x + 8 = 20, x = ?
2x + 8 = 24, x = ?
2x + 8 = 12, x = ?
6x + 9 = 63, x = ?
Step 2 — cross out the sentence with each answer
1.The villain disabled the sonar sensors, then vanished behind a smoke cloud.
2.The villain overrode the security portal, then pointed a laser to jam cameras.
3.The villain switched off the main power, then jammed all radio transmissions.
4.The villain overrode the security portal, then jammed all radio transmissions.
5.The villain overrode the security portal, then blinded the guards with a flash.
6.The villain overrode the security portal, then grappled away into the dark.
7.The villain unlocked the diving airlock, then jammed all radio transmissions.
8.The villain overrode the security portal, then vanished behind a smoke cloud.
9.The villain disabled the sonar sensors, then jammed all radio transmissions.
10.The villain unlocked the diving airlock, then blinded the guards with a flash.
11.The villain drained the ballast tanks, then jammed all radio transmissions.
12.The villain unlocked the diving airlock, then grappled away into the dark.
Solve it
Name the culprit
Choose the one suspect left standing.
Answer Key — The Mystery of the Abyss Engine
Culprit: Cora West (Plasma Cutter · Grappling Hook · Right Handed · Crimson Red Hood · Magnetic Fields)
- Clue 1 (Exponents): "THE VILLAIN DOES NOT USE A LASER POINTER"17^2 = 289 (T) · 9^3 = 729 (P) · 6^2 = 36 (I) · 12^2 = 144 (D) · 2^5 = 32 (U) · 2^4 = 16 (O) · 2^2 = 4 (A) · 19^2 = 361 (R) · 18^2 = 324 (V) · 3^5 = 243 (L) · 20^2 = 400 (S) · 10^2 = 100 (E) · 5^4 = 625 (N) · 5^2 = 25 (H)
- Clue 2 (Square roots): "THE SUSPECT IS RIGHT HANDED"sqrt(289) = 17 (T) · sqrt(25) = 5 (G) · sqrt(324) = 18 (E) · sqrt(625) = 25 (R) · sqrt(169) = 13 (U) · sqrt(4) = 2 (I) · sqrt(100) = 10 (A) · sqrt(256) = 16 (H) · sqrt(225) = 15 (C) · sqrt(49) = 7 (N) · sqrt(484) = 22 (D) · sqrt(196) = 14 (S) · sqrt(361) = 19 (P)
- Clue 3 (Pythagorean theorem): "THE VILLAINS WEAKNESS IS MAGNETIC FIELDS"legs 16 and 30, hypotenuse = 34 (T) · legs 3 and 4, hypotenuse = 5 (K) · legs 24 and 70, hypotenuse = 74 (A) · legs 20 and 48, hypotenuse = 52 (F) · legs 18 and 80, hypotenuse = 82 (L) · legs 32 and 60, hypotenuse = 68 (N) · legs 15 and 36, hypotenuse = 39 (G) · legs 10 and 24, hypotenuse = 26 (S) · legs 15 and 20, hypotenuse = 25 (M) · legs 40 and 42, hypotenuse = 58 (V) · legs 60 and 63, hypotenuse = 87 (W) · legs 24 and 45, hypotenuse = 51 (D) · legs 5 and 12, hypotenuse = 13 (C) · legs 8 and 15, hypotenuse = 17 (H) · legs 9 and 40, hypotenuse = 41 (I) · legs 12 and 35, hypotenuse = 37 (E)
- Clue 4 (Order of operations): "A CRIMSON RED HOOD WAS SEEN ON CAMERA"5 × 11 - 1 = 54 (A) · 10 × 7 - 24 = 46 (D) · 10 × 6 - 13 = 47 (S) · 4 × 12 - 12 = 36 (H) · 3 × 9 - 2 = 25 (I) · 11 × 9 - 9 = 90 (N) · 8 × 9 - 27 = 45 (C) · 7 × 2 - 3 = 11 (M) · 8 × 11 - 1 = 87 (W) · 3 × 7 - 2 = 19 (R) · 11 × 3 - 1 = 32 (O) · 8 + 9 × 5 = 53 (E)
- Clue 5 (Two-step equations): surviving statement (box 12) → Cora West4x + 11 = 23, x = 3 · 3x + 3 = 15, x = 4 · 3x + 1 = 34, x = 11 · 4x + 6 = 26, x = 5 · 5x + 1 = 36, x = 7 · 3x + 1 = 4, x = 1 · 4x + 11 = 51, x = 10 · 2x + 8 = 20, x = 6 · 2x + 8 = 24, x = 8 · 2x + 8 = 12, x = 2 · 6x + 9 = 63, x = 9
About this mystery
- Grade level
- Grade 8 math
- Math topics
- Exponents, Square roots, Pythagorean theorem, Order of operations, Two-step equations
- Reading level
- grades 7-9
- Theme
- The Mystery of the Abyss Engine — set in The Trench Submarine Base
- Format
- Interactive online & printable worksheet with answer key
- Solution
- One unique, verified culprit among 21 suspects