It was a dark and stormy night…

A Warrior, a Scribe, a Builder and a Physician are out walking when night falls and a storm comes up. Lashed by howling gales and freezing rain, they quickly head for shelter. Fortunately the Warrior knows where there is a hut where they can get out of the foul weather, but the path leads across a gorge that is spanned by a rickety bridge. It is a weak bridge, and will collapse if more than two men try to cross it at once.

As it happens, all four of them know this bridge quite well, and have crossed it before. The Warrior knows that he can cross it in one Ehn, the Scribe can manage it in two, the Builder can cross it in five Ehn, but the Physician, who suffers chronic poor health, will take ten full Ehn to cross it. To add to their woes, the lantern that the Builder has brought is failing, and it will go out in precisely seventeen Ehn. With the bridge in its present condition, anyone trying to cross it without the lantern is sure to fall to his death. Therefore at most two men can cross at once – at the speed of the slower man – and someone will have to bring the lantern back for the next journey.

“Do not worry,” declares the Warrior bravely. “I always knew I should some day have to lay down life for those who share my Home Stone, and it might as well be now. You three can surely cross in seventeen Ehn, and I shall take whatever chance I can.”

“Not a bit of it,” says the Physician. “Even you will surely die of exposure if you remain outside on such a night as this. It is my infirmity that imperils us all, and so it is meet that I should stay behind and, by my sacrifice, save three lives.”

“No,” says the Builder, “for if I had provided us with a better lantern, we would be in no danger, and so the whole affair is my responsibility, and I shall stay behind.”

“Heroic,” says the Scribe, “but perhaps we can save our heroism for another day.”

Is the Scribe right in thinking that the four men can cross in seventeen Ehn?