Seven digit base eight positive integer puzzle

In summary, the conversation discusses a seven digit base-8 positive integer, denoted as N, that satisfies certain conditions such as being divisible by 7, 6, 5, 4, 3, and 2. The conversation asks for any possible values of N and also discusses possible methods for solving the problem by hand. The speaker mentions using Excel to calculate values and narrowing down the possibilities through logic.
  • #1
K Sengupta
113
0
N is a seven digit base-8 positive integer having the form ABCDEFG that uses each of the nonzero base-8 digits 1 to 7 exactly once, and satisfies these conditions:

(i) ABCDEFG is divisible by 7.
(ii) ABCDEF is divisible by 6.
(iii) ABCDE divisible by 5.
(iv) ABCD is divisible by 4.
(v) ABC is divisible by 3.
(vi) AB is divisible by 2.

Determine all possible value(s) that N can take.
 
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  • #2
I'm sure I could write a mathematica script to solve this, but does anyone have any good tricks to solve it by hand?
 
  • #3
NeoDevin said:
does anyone have any good tricks to solve it by hand?

I effectively solved by hand (I used Excel to calculate the octal values of stuff), it wasn't too bad. There's only 5040 permutations of 1-7, and the possibilities seemed to cull themselves out pretty quickly. I was able to knock it down to 48 possibilities just using some logic-- from then on it was basically slogging through-- I effectively slogged through 36, but Excel helped.

3254167
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DaveE
 

What is a seven digit base eight positive integer puzzle?

A seven digit base eight positive integer puzzle is a mathematical puzzle that involves finding a seven digit number made up of the digits 0-7 where each digit appears exactly once and the number is divisible by 8.

How do you solve a seven digit base eight positive integer puzzle?

To solve a seven digit base eight positive integer puzzle, you must start by understanding the rules and requirements of the puzzle. Then, you can use trial and error, deductive reasoning, or mathematical equations to find the correct solution.

What is the significance of base eight in this puzzle?

The significance of base eight in this puzzle is that it is a number system that uses eight digits (0-7) instead of the traditional ten digits. This base is commonly used in computer programming and is also known as octal.

Is there a specific strategy or approach to solving this puzzle?

There is no specific strategy or approach to solving a seven digit base eight positive integer puzzle. It ultimately depends on the individual's problem-solving skills and the complexity of the puzzle itself.

Are there any real-world applications for this puzzle?

While the seven digit base eight positive integer puzzle may seem like a purely mathematical exercise, it can have real-world applications in computer science and cryptography. It can also serve as a brain-teaser or educational tool for learning about number systems and problem-solving.

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