An algebra problem by Saikarthik Bathula

Algebra Level 4

Find the number of ordered triples of non-zero integers $(a,b,c)$ such that the product of any two (distinct) elements results in the third element.

2 0 3 4

1 solution

Saikarthik Bathula
May 14, 2014

It is given that, product of two elements results in the third element.... so, aXb=c------(1) & aXc=b------(2) => a(a*b)=b => a^2Xb=b. =>a^2=1 =>a=+1(or)-1 similarly,...b=+1(or)-1 & c=+1(or)-1. therefore,{a,b,c}={1,1,1};{1.-1,-1};{-1,1,-1};{-1,-1,1} are four possible sets ... ans:4

It was pointed out that "sets" is the wrong term to use here, since sets are order independent, and contain distinct entries. As such, I've updated the phrasing to "ordered triples".

Those who previously answered 2 were marked correct. The correct answer is now 4. Sorry to those who got a bunch of emails saying that the answers were corrected. I changed my mind a few times about how to fix this problem.

Calvin Lin Staff - 6 years, 10 months ago

yes answer is 2

Akshay Sharma - 5 years, 6 months ago

Thanks. I see that the problem was edited. Those who answered 2 have been marked correct. I've updated the phrasing of the problem.

Calvin Lin Staff - 5 years, 6 months ago

@Calvin Lin – thanks now satisfied

Akshay Sharma - 5 years, 6 months ago

ans should be 2 only

A Former Brilliant Member - 6 years, 9 months ago

its 4 broo...{1,1,1};{-1,-1,1};{-1,1,-1};{1,-1,-1}

Saikarthik Bathula - 6 years, 8 months ago

you said SET, changing order does not change set

Akshay Sharma - 5 years, 6 months ago

An algebra problem by Saikarthik Bathula

1 solution

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