The Wizard of Saviour
dwarfs numbered to on their T-shirts, are crossing a barrier guarded by a devil. A wizard comes to their rescue by bringing a shuttle of his own. This shuttle can only take dwarfs at a time, and the shuttle does not move if there is no one sitting inside. After each trip, one dwarf must travel back and fetch the others. The devil allows the wizard to use the shuttle on two conditions: The sum of numbers on the T-shirts of the dwarfs travelling at any time must be a perfect square, and the wizard and the devil will not make any trips on the shuttle. What is the minimum number of trips, the dwarfs need to strategize, to cross the barrier?
The answer is 7.
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