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I am finding with some formulas for my web application. I need a formula that counts the number of values between two number, e.g. there are four numbers (3,4,5,6) between 2 and 7

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    $\begingroup$ this problem just might be NP-complete. i hope you have enough computing power to tackle it. $\endgroup$ – Justin L. Dec 8 '10 at 22:54
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larger - smaller - 1. If you don't count the larger and the smaller (like your example).

If the numbers are $n, n+1, \dots, n+k , n+k+1$, the numbers you want are $n+1, n+2, \dots, n+k$, which are $k$ in number = $n+k+1 - n - 1$ = larger - smaller - 1.

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    $\begingroup$ @Cudos: and if your quantities are both integers, and you include all integers between the two in your count, and only integers... $\endgroup$ – Arturo Magidin Dec 8 '10 at 21:23
  • $\begingroup$ @Arturo: Yes, that was the assumption made based on the example. $\endgroup$ – Aryabhata Dec 8 '10 at 21:25
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    $\begingroup$ Not faulting you; I always have to hit my students over the head with the fact that "numbers" doesn't mean "integers and only integers" unless one says so explicitly. $\endgroup$ – Arturo Magidin Dec 8 '10 at 21:26
  • $\begingroup$ @Arturo: Agree with that :-) $\endgroup$ – Aryabhata Dec 8 '10 at 21:28
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HINT $\ $ The problem admits an obvious shift symmetry, e.g. considering the example that you gave, a shift of $-2\:$ to $[3, 6]$ yields $[1,4]$, which clearly has $4$ integers. Innate symmetries should always be investigated since they may play a key role in simplifying the search for a solution. Moreover, it's best to learn these symmetry-based problem solving techniques for simple problems like this, since you may not be able to see the forest for the trees in much more complex problems.

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The number between $a,b$ is $(a<b)$

  • Including $a,b$ them self: $b-a+1$
  • Excluding $a,b$ :$b-a-1$
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The bigger number minus the smaller number minus 1. Or if $b$ is the bigger number, $s$ the smaller. We have: $b - s - 1$

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