2 Amir, Bex, Cerys and Duncan all have birthdays in January. To save money they have decided that they will each buy a present for just one of the others, so that each person buys one present and receives one present. Four slips of paper with their names on are put into a hat and each person chooses one of them. They do not tell the others whose name they have chosen and, fortunately, nobody chooses their own name.
The table shows the cost, in \(\pounds\), of the present that each person would buy for each of the others.
| To | | | |
| \cline { 2 - 6 } | | Amir | Bex | Cerys | Duncan |
| \multirow{4}{*}{From} | Amir | - | 15 | 21 | 19 |
| \cline { 2 - 6 } | Bex | 20 | - | 16 | 14 |
| \cline { 2 - 6 } | Cerys | 25 | 12 | - | 16 |
| \cline { 2 - 6 } | Duncan | 24 | 10 | 18 | - |
| \cline { 2 - 6 } | | | | | |
| \cline { 2 - 6 } |
As it happens, the names are chosen in such a way that the total cost of the presents is minimised.
Assign the cost \(\pounds 25\) to each of the missing entries in the table and then apply the Hungarian algorithm, reducing rows first, to find which name each person chose.