🔎 DetectiveGrade 9Reading: grades 7-9Two-step equationsWord problemsExponentsSquare roots
The Case of the Swapped Crown
A master thief has infiltrated the central archives, swapping the real crown jewels with replicas. As the lead detective on the night shift, you must analyze the forensic evidence, solve the equations left behind in the criminal's notebook, and unmask the Rogue Agent before they board the midnight train.
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 | Sleuthing Tool | Backup Gadget | Signature Handwriting | Ink Stain Color | Tactical Weakness |
|---|---|---|---|---|---|
| C Auguste Dupin | Laser Distance Measurer | Invisible Ink Pen | Right-Tilted Script | Black Ink | Flashlight Glare |
| Sam Spade | Laser Distance Measurer | Miniature Camera | Right-Tilted Script | Blue Ink | Flashlight Glare |
| Joe Hardy | Ultraviolet Torch | Invisible Ink Pen | Left-Tilted Script | Black Ink | Flashlight Glare |
| Hercule Poirot | Pocket Magnifier | Miniature Camera | Right-Tilted Script | Red Ink | Flashlight Glare |
| Nero Wolfe | Directional Microphone | Miniature Camera | Left-Tilted Script | Black Ink | Typewriter Noise |
| Ellery Queen | Pocket Magnifier | Voice Recorder | Left-Tilted Script | Blue Ink | Coffee Aroma |
| Lieutenant Columbo | Laser Distance Measurer | Fingerprint Dust | Right-Tilted Script | Red Ink | Flashlight Glare |
| Sherlock Holmes | Directional Microphone | Voice Recorder | Right-Tilted Script | Blue Ink | Typewriter Noise |
| Perry Mason | Fiber-Optic Camera | Invisible Ink Pen | Right-Tilted Script | Blue Ink | Typewriter Noise |
| Jacques Clouseau | Fiber-Optic Camera | Fingerprint Dust | Right-Tilted Script | Black Ink | Coffee Aroma |
| Jane Marple | Fiber-Optic Camera | Miniature Camera | Left-Tilted Script | Black Ink | Typewriter Noise |
| Miss Scarlet | Pocket Magnifier | Lockpick Set | Right-Tilted Script | Black Ink | Coffee Aroma |
| Professor Plum | Ultraviolet Torch | Fingerprint Dust | Left-Tilted Script | Black Ink | Typewriter Noise |
| Adrian Monk | Fiber-Optic Camera | Voice Recorder | Right-Tilted Script | Black Ink | Coffee Aroma |
| Dick Tracy | Pocket Magnifier | Lockpick Set | Left-Tilted Script | Black Ink | Typewriter Noise |
| Arsene Lupin | Ultraviolet Torch | Invisible Ink Pen | Left-Tilted Script | Black Ink | Typewriter Noise |
| Frank Hardy | Fiber-Optic Camera | Lockpick Set | Right-Tilted Script | Black Ink | Typewriter Noise |
| Philo Vance | Fiber-Optic Camera | Voice Recorder | Left-Tilted Script | Blue Ink | Typewriter Noise |
| Charlie Chan | Ultraviolet Torch | Voice Recorder | Left-Tilted Script | Blue Ink | Typewriter Noise |
| John Watson | Laser Distance Measurer | Invisible Ink Pen | Left-Tilted Script | Red Ink | Typewriter Noise |
| Philip Marlowe | Pocket Magnifier | Fingerprint Dust | Right-Tilted Script | Black Ink | Coffee Aroma |
Clue 1
Two-step equations
We found a torn page from the suspect's logbook. By calculating the total number of evidence boxes they sorted, we can figure out what gadget was missing from their toolbelt.
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
16
10
21
5
11
6
9
6
T
16
7
14
21
20
15
9
2
21
8
18
8
15
9
T
16
11
7
14
T
16
7x + 1 = 113, x =T
7x + 11 = 137, x =P
7x + 11 = 88, x =D
7x + 2 = 51, x =U
5x + 6 = 46, x =R
5x + 6 = 51, x =N
9x + 1 = 136, x =I
9x + 9 = 63, x =O
8x + 11 = 171, x =F
6x + 11 = 71, x =H
6x + 8 = 38, x =Y
3x + 10 = 52, x =S
2x + 11 = 15, x =G
8x + 1 = 169, x =E
0/14 letters found
Clue 2
Word problems
The thief left a locked cryptographic safe. Solving the equation on the keypad reveals the tilt of the handwriting on the ransom note.
Solve each problem to learn its letter, then write the letters in the boxes to fill in the missing word.
Awitnesssawthevillainwas .
L
50
40
25
83
83
64
L
50
83
40
88
117
C
R
64
P
83
Chief Inspector lined up 5 rows of 10 magnifying glasses. How many magnifying glasses in all?L
Chief Inspector found 46 secret dossiers yesterday and 42 more today. How many secret dossiers in all?D
Chief Inspector lined up 8 rows of 8 decoder rings. How many decoder rings in all?I
Chief Inspector found 29 notepad pages yesterday and 88 more today. How many notepad pages in all?S
There were 88 magnifying glasses. 5 were used up. How many magnifying glasses are left?T
Chief Inspector lined up 4 rows of 10 secret dossiers. How many secret dossiers in all?E
Chief Inspector found 5 decoder rings yesterday and 20 more today. How many decoder rings in all?F
0/7 letters found
Clue 3
Exponents
The suspect's getaway path multiplied rapidly. Calculating the exponential growth of the footprints reveals the unique weakness that stops them in their tracks.
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
484
32
49
A
484
32
324
81
441
361
441
25
81
400
128
512
49
25
32
324
400
729
144
128
81
196
216
A
484
729
144
22^2 =A
20^2 =S
21^2 =N
9^3 =T
6^3 =P
12^2 =H
18^2 =K
7^2 =L
5^2 =O
2^7 =E
14^2 =R
2^9 =B
2^5 =C
19^2 =G
9^2 =I
0/15 letters found
Clue 4
Square roots
We discovered a perfect square grid of fingerprint dust. Finding the root of this area points directly to the ink stain color found on the suspect's collar.
Solve each problem to learn its letter. Then write that letter in every box that shows the same number, and read the secret clue.
B
19
21
11
18
10
16
8
13
3
23
20
16
14
20
25
20
21
20
7
17
24
12
17
2
20
3
20
16
10
sqrt(361) =B
sqrt(529) =G
sqrt(169) =U
sqrt(324) =C
sqrt(9) =D
sqrt(121) =A
sqrt(576) =O
sqrt(144) =N
sqrt(441) =L
sqrt(400) =E
sqrt(256) =S
sqrt(625) =R
sqrt(64) =M
sqrt(49) =F
sqrt(289) =T
sqrt(4) =H
sqrt(100) =K
sqrt(196) =W
0/18 letters found
Clue 5
Two-step equations — the last clue
The getaway vehicle's tire pressure sensor displayed a calibrated equation. Solving it unmasks the thief's final weakness.
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
9x + 4 = 94, x = ?
3x + 7 = 34, x = ?
4x + 12 = 60, x = ?
7x + 5 = 26, x = ?
4x + 1 = 9, x = ?
9x + 8 = 17, x = ?
7x + 4 = 60, x = ?
5x + 10 = 30, x = ?
6x + 10 = 52, x = ?
5x + 2 = 27, x = ?
4x + 6 = 30, x = ?
Step 2 — cross out the sentence with each answer
1.The villain intercepted the coded message, then fled across the foggy bridge.
2.The villain intercepted the coded message, then blended into the busy crowd.
3.The villain bypassed the laser grid, then blended into the busy crowd.
4.The villain bypassed the laser grid, then fled across the foggy bridge.
5.The villain intercepted the coded message, then vanished into the rainy night.
6.The villain cracked the master safe, then fled across the foggy bridge.
7.The villain cloned the security badge, then fled across the foggy bridge.
8.The villain cloned the security badge, then blended into the busy crowd.
9.The villain bypassed the laser grid, then escaped in a yellow cab.
10.The villain cracked the master safe, then vanished into the rainy night.
11.The villain intercepted the coded message, then escaped in a yellow cab.
12.The villain swiped the secret files, then fled across the foggy bridge.
Solve it
Name the culprit
Choose the one suspect left standing.
Answer Key — The Case of the Swapped Crown
Culprit: Jane Marple (Fiber-Optic Camera · Miniature Camera · Left-Tilted Script · Black Ink · Typewriter Noise)
- Clue 1 (Two-step equations): "THEY DO NOT USE FINGERPRINT DUST"7x + 1 = 113, x = 16 (T) · 7x + 11 = 137, x = 18 (P) · 7x + 11 = 88, x = 11 (D) · 7x + 2 = 51, x = 7 (U) · 5x + 6 = 46, x = 8 (R) · 5x + 6 = 51, x = 9 (N) · 9x + 1 = 136, x = 15 (I) · 9x + 9 = 63, x = 6 (O) · 8x + 11 = 171, x = 20 (F) · 6x + 11 = 71, x = 10 (H) · 6x + 8 = 38, x = 5 (Y) · 3x + 10 = 52, x = 14 (S) · 2x + 11 = 15, x = 2 (G) · 8x + 1 = 169, x = 21 (E)
- Clue 2 (Word problems): "LEFT TILTED SCRIPT"Chief Inspector lined up 5 rows of 10 magnifying glasses. How many magnifying glasses in all? = 50 (L) · Chief Inspector found 46 secret dossiers yesterday and 42 more today. How many secret dossiers in all? = 88 (D) · Chief Inspector lined up 8 rows of 8 decoder rings. How many decoder rings in all? = 64 (I) · Chief Inspector found 29 notepad pages yesterday and 88 more today. How many notepad pages in all? = 117 (S) · There were 88 magnifying glasses. 5 were used up. How many magnifying glasses are left? = 83 (T) · Chief Inspector lined up 4 rows of 10 secret dossiers. How many secret dossiers in all? = 40 (E) · Chief Inspector found 5 decoder rings yesterday and 20 more today. How many decoder rings in all? = 25 (F)
- Clue 3 (Exponents): "A CLACKING NOISE BLOCKS THEIR PATH"22^2 = 484 (A) · 20^2 = 400 (S) · 21^2 = 441 (N) · 9^3 = 729 (T) · 6^3 = 216 (P) · 12^2 = 144 (H) · 18^2 = 324 (K) · 7^2 = 49 (L) · 5^2 = 25 (O) · 2^7 = 128 (E) · 14^2 = 196 (R) · 2^9 = 512 (B) · 2^5 = 32 (C) · 19^2 = 361 (G) · 9^2 = 81 (I)
- Clue 4 (Square roots): "BLACK SMUDGES WERE LEFT ON THE DESK"sqrt(361) = 19 (B) · sqrt(529) = 23 (G) · sqrt(169) = 13 (U) · sqrt(324) = 18 (C) · sqrt(9) = 3 (D) · sqrt(121) = 11 (A) · sqrt(576) = 24 (O) · sqrt(144) = 12 (N) · sqrt(441) = 21 (L) · sqrt(400) = 20 (E) · sqrt(256) = 16 (S) · sqrt(625) = 25 (R) · sqrt(64) = 8 (M) · sqrt(49) = 7 (F) · sqrt(289) = 17 (T) · sqrt(4) = 2 (H) · sqrt(100) = 10 (K) · sqrt(196) = 14 (W)
- Clue 5 (Two-step equations): surviving statement (box 11) → Jane Marple9x + 4 = 94, x = 10 · 3x + 7 = 34, x = 9 · 4x + 12 = 60, x = 12 · 7x + 5 = 26, x = 3 · 4x + 1 = 9, x = 2 · 9x + 8 = 17, x = 1 · 7x + 4 = 60, x = 8 · 5x + 10 = 30, x = 4 · 6x + 10 = 52, x = 7 · 5x + 2 = 27, x = 5 · 4x + 6 = 30, x = 6
About this mystery
- Grade level
- Grade 9 math
- Math topics
- Two-step equations, Word problems, Exponents, Square roots
- Reading level
- grades 7-9
- Theme
- The Case of the Swapped Crown — set in The Shadowy Streets of London
- Format
- Interactive online & printable worksheet with answer key
- Solution
- One unique, verified culprit among 21 suspects