Seven Fingers

Logic Level 4

$\large \square\square\square \ \div \ \square\square$

You are given that the numbers $1,2,3,4$ and $5$ are to be filled in the square boxes as shown above (without repetition) such that the expression above represent a ratio between a 3-digit integer and a 2-digit integer. Let the resultant number be denoted as $N$ . Find the sum of all possible integer value(s) of $N$ .

The answer is 43.

1 solution

Shib Shankar Sikder
Aug 13, 2015

There will be only 2 cases: 532/14 and 215/43.

I did it by brute force only, but some cases we can reject just by observation such as:

If it is denoted by a/b :

b cannot be 15, 25, 35, 45 as in such cases a have to be divisible by 5 and it is not.

b cannot be 24 or 42, as then a has to be even but it is actually odd.

If last digit of b is 2, last digit of a has to be 4 and vice versa.

In this way lot of cases will get eliminated.

I also did it by brute force, with the same tactics. I hoped there would be a nicer way but perhaps not.

Will Wombell - 5 years, 9 months ago

and i felt stupid using brute force (what a relief :))

Elias Lageder - 4 years, 4 months ago

Seven Fingers

The answer is 43.

1 solution

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