Solution
The ten puzzles are attempted in one fixed sequence that is common to all four competitors, so puzzle is the same type (visual or number-based) for everyone.
Left chart (puzzles solved vs time): the instant a competitor's count steps up to is the time at which that competitor finished puzzle . These give the cumulative completion times.
Right chart (visual puzzles solved vs time): comparing how the visual count rises against how the total count rises identifies each puzzle as visual () or number-based ().
The table records the type of each puzzle and each competitor's cumulative completion time (in minutes). From it we can read how many puzzles anyone had finished at any instant, and the time spent on a single puzzle as the gap between consecutive completion times.
| Puzzle | Type | Anirbid | Chandranath | Koushik | Suranjan |
|---|---|---|---|---|---|
| 1 | |||||
| 2 | |||||
| 3 | |||||
| 4 | |||||
| 5 | |||||
| 6 | |||||
| 7 | |||||
| 8 | |||||
| 9 | |||||
| 10 |
| Puzzle | Type | Anirbid | Chandranath | Koushik | Suranjan |
|---|---|---|---|---|---|
| 1 | 2 | ||||
| 2 | 4 | ||||
| 3 | 6 | ||||
| 4 | 8 | ||||
| 5 | 10 | ||||
| 6 | 12 | ||||
| 7 | 14 | ||||
| 8 | 16 | ||||
| 9 | 19 | ||||
| 10 | 22 |
Koushik's completion times are read from the left chart.
His line steps up by one puzzle about every minutes early on and slows near the end, reaching:
His steady, clean steps make him the most reliable line to read first.
| Puzzle | Type | Anirbid | Chandranath | Koushik | Suranjan |
|---|---|---|---|---|---|
| 1 | V | 2 | |||
| 2 | N | 4 | |||
| 3 | V | 6 | |||
| 4 | N | 8 | |||
| 5 | N | 10 | |||
| 6 | N | 12 | |||
| 7 | V | 14 | |||
| 8 | V | 16 | |||
| 9 | V | 19 | |||
| 10 | V | 22 |
The Type column is filled using the right chart for Koushik.
His visual-puzzle count at each completion instant is:
after P1:
after P2:
after P3:
after P4:
after P5:
after P6:
after P7:
after P8:
after P9:
after P10:
The visual count increases exactly at puzzles , so these are visual ().
It stays unchanged at puzzles , so these are number-based ().
This gives total visual and total number-based . The other three competitors' charts reproduce the same pattern, confirming the common sequence.
| Puzzle | Type | Anirbid | Chandranath | Koushik | Suranjan |
|---|---|---|---|---|---|
| 1 | V | 3 | 2 | ||
| 2 | N | 7 | 4 | ||
| 3 | V | 10 | 6 | ||
| 4 | N | 13 | 8 | ||
| 5 | N | 18 | 10 | ||
| 6 | N | 22 | 12 | ||
| 7 | V | 24 | 14 | ||
| 8 | V | 26 | 16 | ||
| 9 | V | 28 | 19 | ||
| 10 | V | 31 | 22 |
Anirbid's completion times are read from the left chart:
He finishes last overall, with all ten done at minute .
| Puzzle | Type | Anirbid | Chandranath | Koushik | Suranjan |
|---|---|---|---|---|---|
| 1 | V | 3 | 4 | 2 | |
| 2 | N | 7 | 7 | 4 | |
| 3 | V | 10 | 10 | 6 | |
| 4 | N | 13 | 13 | 8 | |
| 5 | N | 18 | 16 | 10 | |
| 6 | N | 22 | 19 | 12 | |
| 7 | V | 24 | 22 | 14 | |
| 8 | V | 26 | 24 | 16 | |
| 9 | V | 28 | 26 | 19 | |
| 10 | V | 31 | 28 | 22 |
Chandranath's completion times are read from the left chart:
| Puzzle | Type | Anirbid | Chandranath | Koushik | Suranjan |
|---|---|---|---|---|---|
| 1 | V | 3 | 4 | 2 | 3 |
| 2 | N | 7 | 7 | 4 | 6 |
| 3 | V | 10 | 10 | 6 | 10 |
| 4 | N | 13 | 13 | 8 | 13 |
| 5 | N | 18 | 16 | 10 | 16 |
| 6 | N | 22 | 19 | 12 | 20 |
| 7 | V | 24 | 22 | 14 | 22 |
| 8 | V | 26 | 24 | 16 | 24 |
| 9 | V | 28 | 26 | 19 | 26 |
| 10 | V | 31 | 28 | 22 | 29 |
Suranjan's completion times are read from the left chart:
The table is now complete. Every type and completion time is fixed by the two charts, with no ambiguity.
The puzzle sequence is (visual at ; number-based at ).
Total times are Koushik , Chandranath , Suranjan , Anirbid , so Koushik is the winner.
From the sequence, visual puzzles occupy positions . Hence the third visual puzzle is puzzle .
Suranjan finished puzzle at minute and puzzle at minute .
Time on the third visual puzzle minutes.
Answer: 2.
More from this set:
Question 6