Ye olde webbe connection: The Wknd Puzzle by Dilip D’Souza

How many cottages is the right number of cottages for this quaint English village, given that they now want to talk to one another using a phone-based intercom network?

This puzzle is being written up — by me, I confess — on a train barrelling north through the English countryside. We’ve zipped through a few villages, and I remembered a particularly picturesque one we visited a week ago: Adlestrop, famous for a poem (look it up), the village consisting of no more than 20 or 25 cottages. Call it 25.

(Shutterstock)

I also got to thinking about phones. Imagine that Adlestrop is stuck in a time warp and nobody there has cellphones. But the residents want to be connected to each other, so they decide to set up a phone-based intercom network. Each of the 25 houses gets a simple phone, and the plan is to connect each phone with wires to exactly five other phones; ie, each of the 25 cottages will have five wires radiating from it.

Can the village accomplish this?

What if Adlestrop had only 20 cottages?

Scroll down for the answer.

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Answer:

No, with 25 cottages this is impossible. Imagine that each phone has five outlets for wires. So we have a total of 125 (25 x 5) outlets. Each wire connects two outlets. So how many wires do we need? 125 / 2 = 62.5. Not possible.

But if the village had only 20 cottages, we’d have a total of 100 (20 x 5) outlets. Now we need 100 / 2 = 50 wires. Certainly possible.