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Bergerac | ||||

$87$ | Bordeaux | |||

$79$ | $47$ | Langon | ||

$61$ | $31$ | $54$ | Libourne | |

$58$ | $84$ | $37$ | $65$ | Marmande |

The table shows the distance (in $\text{km}$) between five towns in southern France. Five friends live in these five towns and want to meet. In which of these towns should they meet to keep the total travelling distance as small as possible?

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*This problem is taken from the UKMT Mathematical Challenges.*

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