# Count number of values between two numbers

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

• this problem just might be NP-complete. i hope you have enough computing power to tackle it. – Justin L. Dec 8 '10 at 22:54

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.

• @Cudos: and if your quantities are both integers, and you include all integers between the two in your count, and only integers... – Arturo Magidin Dec 8 '10 at 21:23
• @Arturo: Yes, that was the assumption made based on the example. – Aryabhata Dec 8 '10 at 21:25
• 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. – Arturo Magidin Dec 8 '10 at 21:26
• @Arturo: Agree with that :-) – Aryabhata Dec 8 '10 at 21:28

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.

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

• Including $a,b$ them self: $b-a+1$
• Excluding $a,b$ :$b-a-1$

The bigger number minus the smaller number minus 1. Or if $b$ is the bigger number, $s$ the smaller. We have: $b - s - 1$