Reworded UKMT Intermediate Challenge

Logic Level 4

A road from Alphaville to Echoton passes through three other towns: Bravoton, Charlyville and Deltatown in that order. The distances along the road between pairs of these towns are given in kilometres. From smallest to largest, these ten distances are \(2, 5, 6, *, *, *, *, 15, 18, 20\). Find all possible missing distances. Input the sum of all possible distances (for example, if we had possibilities \(7,8,9,10\); \(7,8,13,14\) and \(11,12,13,14\) the input would be \(7+8+9+10+7+8+13+14+11+12+13+14\)).

This is an altered problem from the 2015 UKMT Grey Intermediate Kangaroo Paper.
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