If you have to put n 1 pigeons into n holes, you have to put two pigeons into the same hole. What happens if you have to put m n 1 pigeons into n holes?

Question

07-02-2020
Mathematics

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If you have to put n 1 pigeons into n holes, you have to put two pigeons into the same hole. What happens if you have to put m n 1 pigeons into n holes?

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olumidechemeng olumidechemeng · Answer 1 · 2020-02-09T19:54:17+01:00

Answer:

Making an assumptions that i have n holes and exactly nm pigeons, this implies tat there is a possibility of me putting m pigeons occupying each hole. now if i add one more pigeons, it implies that, there will be a contradiction and as such, one of the holes will have an additional m+1 pigeons in n holes.

Making sure that every hole has to contain m pigeons, as such the rest m+1 pigeons will occupy n-1 holes which will have mn+1 pigeons in totality.

Step-by-step explanation:

Making an assumptions that i have n holes and exactly nm pigeons, this implies tat there is a possibility of me putting m pigeons occupying each hole. now if i add one more pigeons, it implies that, there will be a contradiction and as such, one of the holes will have an additional m+1 pigeons in n holes.

making sure that every hole has to contain m pigeons, as such the rest m+1 pigeons will occupy n-1 holes which will have mn+1 pigeons in totality/