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.
I also got to thinking about phones. Imagine that Adlestrop is stuck in a time warp and nobody there
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.
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.
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