Claudette's Exploding Bridge Conundrum

Jul 16, 2007

RAY: This was sent in by John Head. I had to obfuscate and de-clarify, but I think it's now satisfactory.

"It was a dark, moonless night in France, 1943, deep within German-held territory. Out of the inky shadows comes Claudette, the beautiful French resistance fighter, followed by three downed Allied crew members, who she must get back into friendly hands. They must cross a bridge, and they know the Germans are not far behind. It's an old, treacherous bridge, and they have only one flashlight among them to see. The bridge can support only two of them at a time. Three on the bridge, and it's curtains.

"Pairs crossing can do so only as quickly as the slower member of the pair, because they need the flashlight to see. Each time a pair crosses, someone has to return with the flashlight, until they're all safely across.

"Unfortunately, the three downed airmen are injured. Here are the times each person takes to cross the bridge: Claudette can do it in a minute. Major Johnson has a twisted ankle, and takes 2 minutes. Captain Kangaroo got shot up pretty bad. He has to hop on one foot, and it takes him 5 minutes. Colonel Mustard is in worse shape. It takes him 10 minutes to cross the bridge.

"Claudette has rigged the bridge with explosives so that their pursuers can't follow. She's about to set the timer."

Here's the puzzler: What's the shortest time she can set and get everyone safely across the bridge before it blows up?
RAY: The secret is that you want the fastest people making the greatest number of crossings. So, Claudette and Johnson, who can do it in one and two minutes, respectively, cross together. That takes two minutes.

One of them comes back, let's say it's Johnson, that takes another 2 minutes. Okay, now she's on the good side of the bridge and Johnson isn't.

TOM: So now we got the two slow guys on the wrong side of the bridge, along with Major Johnson.

RAY: Johnson stays there and the two slow guys hop over the bridge. That takes 10 minutes. Okay, so now we're up to 14 minutes.

Claudette dashes across the bridge with the flashlight-- that takes a minute, right? She and Johnson cross together.

TOM: That takes two minutes.

RAY: That's 17 minutes. They got across in 17 minutes, when bingo, the bridge blows up! The Germans are sitting there saying, "Sonja Henie's tutu!"

TOM: That's a good puzzler, because there's a tendency to want Claudette to make lots of trips but she shouldn't.

RAY: I think it's pretty cute.

Get the Car Talk Newsletter