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A combinatorics problem on connecting the cities 
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#1
Dec1712, 05:21 AM

P: 31

Fifteen cities are planned to be connected in such a way that each city has precisely one road leading to each of five other cities.How many such roads are to be constructed?
This question was asked in a talent test conducted in our school. 


#2
Dec1712, 10:49 AM

P: 403

5*15=75 which is not an even number. So it is impossible.



#3
Dec1912, 07:38 AM

P: 31

Can you explain me clearly why is it impossible? 


#4
Dec1912, 08:16 AM

Mentor
P: 11,925

A combinatorics problem on connecting the cities
Assuming that a road always leads from one city to another city, each city has 5 road ends connected to this city, so we have a total of exactly 75 road ends.
Every road has 2 ends  the total number of road ends has to be even. 75 is not even. 


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