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BMAD

How Low can U go?

Question

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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12 answers to this question

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a = 1, b = 9, c = 9 for a minimum value of 10.473684210526315

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a = 1, b = 9, c = 9 for a minimum value of 10.473684210526315

there is a smaller answer

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...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...
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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!
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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

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...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

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I get

a = -9

b = 1

c = 9

100*a + 10*b +1*c = M = -881

M/(a+b+c) = -881

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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 by BMAD
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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 by Rob_Gandy
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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!

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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 by BMAD
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I ran a program which suggests that the answer is 10.47 at M=199.

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