PRMO Problem (I found it online)
x , y , z are distinct non-negative integers such that x y + z = 1 6 0 . Find the least possible value of x + y z .
The answer is 1.
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1 solution
Hi, you should mention that x , y and z are distinct postive integers, as else x = y = 0 and z = 1 6 0 gives answer 0 .
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Thanks. I've updated the answer to
0
. Those who previously answered
0
has been marked correct.
In the future, if you have concerns about a problem's wording/clarity/etc., you can report the problem. See how here .
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Thanks, but that wasn't to be the problem. I actually forgot to mention 'distinct' non-negative integers :)
Please change the answer back to normal, as I have edited the problem.
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@A Former Brilliant Member – Done.
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@Brilliant Mathematics – Thanks for the help!
@Brilliant Mathematics – Looks like there is a glitch. I had answered 1 initially which was taken as correct, but when the answer was changed to 0 it was then considered incorrect. Now the answer is back to 1, but my initial try of 1 is not considered correct and I can’t re-answer with 1 (I tried 0 and 50 on my next two attempts just to see what would happen). Not a big deal but I’m guessing others are experiencing the same issue.
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@A Former Brilliant Member – Hi Brian, I've given you credit for answering this problem.
If instead the integers must be positive rather than simply non-negative I find a minimum of 50, with x = 26, y = 6, z = 4.
Non negative, so they can be 0.
If y = 0, then whatever x is, z needs to be 160. The least possible value for x is 1, as y is already 0, so x = 1 and z = 160.
x + yz computes to 1, which is our answer.