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15 Telephone Boxes

A new technician starts work as a telephone repair man. There are 15 telephone boxes in his section, shown below (ok, this teaser is quite old !). On his first day, the foreman tells the new technician that five out of the first eight boxes need repairing and that he should go and repair one as an initial test of his workmanship.

The new technician goes straight to ‘phone box number eight. Why ?

because it was the nearest box to the technician.

Because it wasn’t working.

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I’m afraid not, Steve.

Of course, in any other scenario, that might be the case, but remember, the supervised stated that “five of the first eight” were in need of repair. The nearest one might not have been one of those five.

Technically you are correct Mike.

But what was the number of that phone box and how did the technician know that it was in need of repair.?

This teaser involves a bit of “latent trust” between Supervisor and Technician.

It’s not as straightforward as 2+2=4, but there is an inferred (or should that be implied) condition in what the Supervisor has said.

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Because the boxes have a unique number (1 through to 15) and there are 5 of the “number 8” boxes that need fixing?

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Not quite, Mike. But you are probably heading in the right direction.

The Boxes are numbered 1 thu’ 15 as shown in the diagram. The Supervisor has (helpfully) said that …

I would add that the New technician, based on what the Supervisor had said, was certain that the box he chose, did actually need to be repaired !

Because if number 8 was working, the supervisor would have said 5 of the first 7 aren’t working?

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Ah yes, as he has said “of the first 8” then the 5th to not be working must be the eight one. Well done Sir.

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Nicely sorted Dozey.

A good tries by Steve and Mike.

That wasn’t one of my favourite types of Teasers, but lots of people do seem to like these rather vague, but carefully worded offerings.

Well done to all those who gave it a shot !

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It’s a very clever question, and I’m very impressed Dozey got it. I wish I’d seen it, especially after you gave us subtle but clear clues.

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I find logic easier than the more mathematical questions!

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You won’t enjoy the next one then Dozey :sunglasses:

But well done on the telephone Boxes !!

26.18 sq cm

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Bigger circle area is 225xPi
Each smaller circle is 25xPi
7 smaller circles, so 175xPi
So the “non-small-circle” inside the big circle is 50xPi.
There are 6 identical spaces between circles and outer circle, so the shaded space is 50/6 x Pi = 25/3x Pi

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Well done to both Steve and Eoink, especially given the answers obviously came within a few minutes of posting the teaser !

I’ve known one or two people presume there were seven areas between the circles, rather than just the six.

I noticed that Dozey “liked” one of the replies, i’m wondering if my “prediction” - “You won’t enjoy the next one then Dozey”, was embarrassingly wide of the mark, as I rather suspect !

I liked this one, because as Eoink pointed out, it can be done analytically using algebra without actually having to do the arithmetic, or having to remember geometric theorems.

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