Can You Count the Zeros Between Two Numbers?

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Discussion Overview

The discussion revolves around the mathematical determination of how many zeros appear between two integers, inclusive of those integers. Participants explore various approaches to this problem, considering both mathematical theories and computational methods.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant inquires about a mathematical method to count zeros between two numbers, providing an example with integers 10 and 12.
  • Another participant suggests a combinatorial approach as a simple solution.
  • A different participant expresses confusion, interpreting "zeros" as the roots of a function rather than counting zero digits in numbers.
  • Another suggestion involves treating each number as a string to count zero characters, proposing a formula to calculate the number of zeros in a range based on a sequence.
  • A later reply clarifies that the zeros in question refer to zero digits within the numbers themselves.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the interpretation of "zeros" or the best method to count them, indicating multiple competing views and unresolved questions.

Contextual Notes

There is ambiguity regarding the definition of "zeros" and whether the discussion pertains to counting zero digits or identifying mathematical zeros of functions. The proposed methods also vary in their assumptions and applicability.

whatever84
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Dear all,

Can anybody tell me if there is any mathematical way to know how many zeros between a and b, where we should consider all the numbers between them (inclusive).

E.g.

a = 10,
b = 12,

numbers in between: 10, 11, 12

Thus, the answer is --> 1

I made a simple program to do this for me by looping and incrementing, but as the numbers become bigger, it take "long" time to get the result.

Thus, math theories might be the solution for such problem.

Thanks
 
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Yes, and it is simple. Use a combinatorial aproach.
 
whatever84 said:
Dear all,

Can anybody tell me if there is any mathematical way to know how many zeros between a and b, where we should consider all the numbers between them (inclusive).

E.g.

a = 10,
b = 12,

numbers in between: 10, 11, 12

Thus, the answer is --> 1

I made a simple program to do this for me by looping and incrementing, but as the numbers become bigger, it take "long" time to get the result.

Thus, math theories might be the solution for such problem.

Thanks
I don't understand what you mean. When you say "zeros" I assume you mean the zeroes of some function, but your example appears to be how many integers there are between two given integers.
 
whatever84 said:
Dear all,

Can anybody tell me if there is any mathematical way to know how many zeros between a and b, where we should consider all the numbers between them (inclusive).

E.g.

a = 10,
b = 12,

numbers in between: 10, 11, 12

Thus, the answer is --> 1

I made a simple program to do this for me by looping and incrementing, but as the numbers become bigger, it take "long" time to get the result.

Thus, math theories might be the solution for such problem.

Thanks
If you mean look at each number as a string and count how many characters are zero I think you should try for solving in general generate a(n) = the number of zeros in [1, n] then [b,c] = a(c) - a(b-1). See http://www.research.att.com/~njas/sequences/A061217
 
Last edited by a moderator:
Oh, zero digits.
 

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