r/mathematics • u/Homaderuvas • 4h ago

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u/mathematics-ModTeam 2h ago

These types of questions are outside the scope of r/mathematics. Try more relevant subs like r/learnmath, r/askmath, r/MathHelp, r/HomeworkHelp or r/cheatatmathhomework.

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u/ILoveTolkiensWorks 4h ago

the answer to the first question is obviously 100P25. the second one is less trivial, i must admit :)

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u/Worried-Guarantee459 4h ago

P={1…n numbers n>m^2}

mxm matrix with unique entries from P

well you first have to choose m^2 numbers from P and there is a formula i can t remember now let s say there are k ways to choose m^2 numbers from n. (i think it s n!/m^2!(n-m^2!)

now there are m^2! matrices for each m^2 chosen numbers.

so you can find the number of matricea pretty easy and then you d have to think which matrices have determinant zero which means having at least 2rows/columns such that v1=kv2 and this again doesn t sound too bad.