BMAD 65 Posted May 20, 2013 Report Share Posted May 20, 2013 suppose there is a three digit number M where 100*a + 10*b +1*c = M where a, b, and c are digits What is the minimum value that can be found from M/(a+b+c)? 1 1 Quote Link to post Share on other sites

0 Solution Pickett 13 Posted May 20, 2013 Solution Report Share Posted May 20, 2013 a = 1, b = 9, c = 9 for a minimum value of 10.473684210526315 1 Quote Link to post Share on other sites

0 BMAD 65 Posted May 20, 2013 Author Report Share Posted May 20, 2013 a = 1, b = 9, c = 9 for a minimum value of 10.473684210526315 there is a smaller answer Quote Link to post Share on other sites

0 Pickett 13 Posted May 20, 2013 Report Share Posted May 20, 2013 ...assuming a doesn't equal 0 (since that would mean it isn't truly a three digit number) I'd be curious to see a smaller value of M / (a + b + c) I'm going to stick by 199/19 = 10.473684210... Quote Link to post Share on other sites

0 Pickett 13 Posted May 20, 2013 Report Share Posted May 20, 2013 Alright, I realized my mistake...here ya go: a = 0.39 b = 5.2 c = 9 Gives you a 3 digit number of 100, but a min value of 6.854009595613435 Nice puzzle! Quote Link to post Share on other sites

0 BMAD 65 Posted May 20, 2013 Author Report Share Posted May 20, 2013 Alright, I realized my mistake...here ya go: a = 0.39 b = 5.2 c = 9 Gives you a 3 digit number of 100, but a min value of 6.854009595613435 Nice puzzle! a, b, c are digits Quote Link to post Share on other sites

0 BMAD 65 Posted May 20, 2013 Author Report Share Posted May 20, 2013 ...assuming a doesn't equal 0 (since that would mean it isn't truly a three digit number) I'd be curious to see a smaller value of M / (a + b + c) I'm going to stick by 199/19 = 10.473684210... you are right in that a does not equal to zero but there is still a smaller answer Quote Link to post Share on other sites

0 BobbyGo 7 Posted May 20, 2013 Report Share Posted May 20, 2013 I get a = -9 b = 1 c = 9 100*a + 10*b +1*c = M = -881 M/(a+b+c) = -881 Quote Link to post Share on other sites

0 BMAD 65 Posted May 20, 2013 Author Report Share Posted May 20, 2013 (edited) I get a = -9 b = 1 c = 9 100*a + 10*b +1*c = M = -881 M/(a+b+c) = -881 a b and c are digits not integers, good idea though. If they were integers there would still be smaller answer then what you have found here. can you find that answer too? Edited May 20, 2013 by BMAD Quote Link to post Share on other sites

0 Rob_Gandy 2 Posted May 21, 2013 Report Share Posted May 21, 2013 (edited) a=-9 b=0 c=9 d= -infinity and any similar variation. I also get a=1 b=9 c=9 d=10.47368..... with the help of Java I get a = -9 b = 1 c = 9 100*a + 10*b +1*c = M = -881 M/(a+b+c) = -881 a b and c are digits not integers, good idea though. If they were integers there would still be smaller answer then what you have found here. can you find that answer too? Edited May 21, 2013 by Rob_Gandy Quote Link to post Share on other sites

0 BMAD 65 Posted May 21, 2013 Author Report Share Posted May 21, 2013 a = 1, b = 9, c = 9 for a minimum value of 10.473684210526315 i found an error in my calculation using 189/18 = 10.5 oops nice work! 1 1 Quote Link to post Share on other sites

0 BMAD 65 Posted May 21, 2013 Author Report Share Posted May 21, 2013 (edited) a=-9 b=0 c=9 d= -infinity and any similar variation. I also get a=1 b=9 c=9 d=10.47368..... with the help of Java I get a = -9 b = 1 c = 9 100*a + 10*b +1*c = M = -881 M/(a+b+c) = -881 a b and c are digits not integers, good idea though. If they were integers there would still be smaller answer then what you have found here. can you find that answer too? I disagree with your first solution (well) since it is undefined, we don't know if the value is defined to mean min or max as it is undefined Edited May 21, 2013 by BMAD 1 1 Quote Link to post Share on other sites

0 James33 1 Posted May 25, 2013 Report Share Posted May 25, 2013 I ran a program which suggests that the answer is 10.47 at M=199. Quote Link to post Share on other sites

## Question

## BMAD 65

suppose there is a three digit number M where 100*a + 10*b +1*c = M where a, b, and c are digits

What is the minimum value that can be found from M/(a+b+c)?

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