Don't make mistakes! #6

Number Theory Level 4

There are three positive integers p , q , r p,~q,~r that satisfy:

  • p ≠ q ; p\neq q;

  • q ≠ r ; q\neq r;

  • p + q + r = 23. p+q+r=23.

Find the maximum of p q r . pqr.

This problem is a part of <Don't make mistakes!> series .

448 400 ( 23 3 ) 3 \left(\dfrac{23}{3}\right)^3 450 432

Boi (보이) by Boi (보이) , 19, South Korea

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1 solution

Boi (보이)
Jul 18, 2017

The question said p ≠ q ≠ r , p\neq q\neq r, not that p , q , r p,~q,~r are distinct.

Therefore, we cannot say that p ≠ r . p\neq r.

For the maximum of p q r pqr to occur, the three integers must be as similar as possible.

Therefore, p q r pqr has its maximum of 448 \boxed{448} at p = 8 , q = 7 , r = 8. p=8,~q=7,~r=8.

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Did the same way.

Niranjan Khanderia - 3 years, 10 months ago

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