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 ?
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.
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
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.