September 2011

# Solution

I had four parrots and three cages.

If you put one parrot in each cage, you have an extra bird without a cage. However, if you put two parrots in each cage, then you have an extra cage.

Let there be x birds and y cages, then we get the following equations:

y=x-1 (because the number of cages is one less than the number of birds)

and 2(y-1)=x (because two birds in one cage will lead to one extra cage, that is y-1 cages will be required to house x birds).

Solving, we get x=4 and y=3.

Some useful links for

• Union Public Service Commission - www.upsc.gov.in
• IIT-Kharagpur - www.iitkgp.ac.in
• Indian Statistical Institute - www.isical.ac.in
• Indian Institute of Technology Madras - www.iitm.ac.in
• Indian Institute of Management, Ahmedabad - www.iimahd.ernet.in
• Indian Institute of Mass Commission - www.iimc.nic.in
• IIT Bombay - www.iitb.ac.in
• Indian School of Mines, Dhanbad - www.ismdhanbad.ac.in
• Birla Institute of Technology, Ranchi - www.bitmesra.ac.in
• Central Institute of Fisheries Nautical and Engineering Training - www.cifnet.nic.in
• Indian Institute of Information Technology, Allahabad (Deemed University) - www.iiita.ac.in
• Central Marine Fisheries Research Institute, Kochi - www.cmfri.com
• Tata Institute of Social Sciences, Mumbai - www.tiss.edu

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