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Sunday Puzzle-24

User Rating: / 4
Written by Administrator   
Sunday, 28 October 2012

Puzzle courtesy of Barry R. Clarke, columnist for The Daily Telegraph and international puzzle expert

Olivers Didgeridoo

Oliver Hoot had just bought a didgeridoo. However, the sound seemed a bit muffled, and although the thing would didger it just wouldn't do. Back at the shop he bought it from, the shopkeeper discovered the problem: a cuckoo was lodging in the pipe. So he blew down one end to drive it out. 

Now the three distances, of the cuckoo from each of the two ends and the pipe length, were all non-prime whole numbers (inches). Also the cuckoo would have taken the same time to fly to one end with the wind speed added to his natural speed as it would have taken to fly to the other end with the wind speed subtracted. It turned out that the cuckoo's natural speed divided by the wind speed was a square number less than 100, numerically equal to the pipe length. How long was Oliver's didgeridoo?
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Comments (5)
1. Written by This e-mail address is being protected from spam bots, you need JavaScript enabled to view it on 02:33 30 2012 .
There are 3 solutions to Barry's puzzle: 
64, 36 or 16 
Cuckoo's speeds: 8, 6 or 4 ; wind's: 1 
8/1 = 8: 8^2 = 64 
6/1 = 6: 6^2 = 36 
4/1 = 4: 4^2 = 16 
Email me if you need more...
2. Written by Peter on 07:39 30 2012 .
@Denis "It turned out that the cuckoo's natural speed divided by the wind speed was a square number less than 100" - 8 and 6 don't fit. Not to mention other conditions...
3. Written by This e-mail address is being protected from spam bots, you need JavaScript enabled to view it on 09:37 30 2012 .
Thanks Peter. I was (erroneously) using the square root as equal to natural/wind. My bad.
4. Written by This e-mail address is being protected from spam bots, you need JavaScript enabled to view it on 10:20 30 2012 .
Sorry, forgot to post corrected version. 
Solution is length = 49 
Easy enough:  
c=cuckoo speed, w=wind speed 
a=distance against wind, b=with wind 
a/(c-w) = b/(c+w) : c = w(a+b)/(b-a) [1] 
c/w=a+b : c = w(a+b) [2] 
[1][2]: b-a = 1  
From there, it's a breeze! 
Of course,without the prime restriction, 
there are 3 other solutions: 
a=4,b=5 : 9 
a=12,b=13 : 25 
a=40,b=41 : 81
5. Written by on 08:29 23 2013 .

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