It's only another flesh wound Part 2

Logic Level 3

\large \square\square \ - \ \square\square \ - \ \square\square

You are given that the numbers 1 , 2 , 3 , 4 , 5 , 6 1,2,3,4,5,6 are to be filled in the square boxes as shown above (without repetition) such that it represents a 2 digit integer subtracting two 2-digit integers.

Of all 6 ! = 720 6!=720 possible arrangements, find the largest negative resultant number.

Details and Assumptions

As an explicit example, we can have 16 34 52 = 70 16 - 34 - 52 = -70 and 12 53 64 = 105 12-53-64=-105 as a resultant number. We will choose the formal answer of 70 -70 because 105 < 70 -105<-70 .

See Part 1 .


The answer is -1.

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8 solutions

46 12 35 = 1 46-12-35=\boxed{-1}

I got 12-64-53=-105... I thought you were looking for a large negative... As in most negative. This isn't so clear

James Cardus - 5 years, 10 months ago

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Yes. I thought exactly the same thing!

Amanda Bini - 5 years, 10 months ago

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me too. we were in the same school of thought.

James Tumusiime - 5 years, 10 months ago

How would you make it clearer?

Chung Kevin - 5 years, 10 months ago

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Maybe say it should be a negative number of smallest magnitude, or that by larger you mean closer to 0

James Cardus - 5 years, 10 months ago

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@James Cardus The question is clear. It may be written as thus in order to maybe trick some people, but it is written correctly. The largest negative number is -1 (I at first put in -105, but that is why we have three tries at problems)

Chris Hambacher - 5 years, 10 months ago

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@Chris Hambacher I guess I just associate the term 'largest' with magnitude. I'm not great with semantics so you're probably right ;)

James Cardus - 5 years, 10 months ago

You could say 'smallest negative integer for which x |x| is minimized;'

Vishnu Bhagyanath - 5 years, 9 months ago

Yeah! exactly....The question was vague.

Brijesh Nair - 5 years, 9 months ago

Thanks. I've updated the problem statement for clarity. Those who previously answered -105 will be marked correct.

Brilliant Mathematics Staff - 5 years, 9 months ago

The same happened to me.

Elena Gomes - 5 years, 10 months ago

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Same for me !

Sylvain Pelloquin - 5 years, 10 months ago

The largest negative is 1 -1 , so I tried and found that 46 12 35 = 1 46-12-35=\boxed{-1}

64-52-13=-1

Adrian Adrian
Aug 24, 2015

64 - 53 - 12 = -1

Clearly, 65-43-21 = 1. Swapping out that 5 and 3's position, we have 63-45-21=-3. Therefore, the answer must be either -1, -2, or -3. You have 3 guesses and can try all 3 answers.

Hrishik Mukherjee
Aug 21, 2015

46 - 35 - 12 = -1

Akash Singh
Aug 18, 2015

64-53-12=-1

and a nice trap for largest -ve integer

P C
Aug 13, 2015

64-53-12 = -1

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