2 In an investigation into a burglary, Agatha has five suspects who were all known to have been near the scene of the crime, each at a different time of the day. She collects evidence from witnesses and draws up a table showing the number of witnesses claiming sight of each suspect near the scene of the crime at each possible time.
Suspect
\begin{table}[h]
\captionsetup{labelformat=empty}
\caption{Time}
| | 1 pm | 2 pm | 3 pm | 4 pm | 5 pm |
| Mrs Rowan | \(R\) | 3 | 4 | 2 | 7 | 1 |
| Dr Silverbirch | \(S\) | 5 | 10 | 6 | 6 | 6 |
| Mr Thorn | \(T\) | 4 | 7 | 3 | 5 | 3 |
| Ms Willow | \(W\) | 6 | 8 | 4 | 8 | 3 |
| Sgt Yew | \(Y\) | 8 | 8 | 7 | 4 | 3 |
\end{table}
- Use the Hungarian algorithm on a suitably modified table, reducing rows first, to find the matchings for which the total number of claimed sightings is maximised. Show your working clearly. Write down the resulting matchings between the suspects and the times.
Further enquiries show that the burglary took place at 5 pm , and that Dr Silverbirch was not the burglar.
- Who should Agatha suspect?