Method For Determining if a Series of Integers Is Sequential or Not

I’m sure this must be a well known mathematical trick, but I actually figured this one out myself, so I’m understandably astonished:

I’ve discovered a neat math shortcut for determining whether or not an arbitrary group of integers are sequential (that is, if there are any gaps in the numbers).

A group of unique integers is sequential if the difference between the largest integer and the smallest integer is equal to one less than the total number of integers.

Here are some examples:

e.g. 1

1,2,3,4,5

largest = 5

smallest = 1

largest – smallest = 5 – 1 = 4

count – 1 = 5 – 1 = 4

largest – smallest = count – 1 , therefore, the series is sequential

e.g. 2

1,2,3,4,6

largest = 6

smallest = 1

largest – smallest = 6 – 1 = 5

count – 1 = 5 – 1 = 4

largest – smallest ≠ count – 1 , therefore, the series is not sequential

e.g. 3

-3, -2, -1

largest = -1

smallest = -3

largest – smallest =-3 – -1 = -3 + 1 = -2

count – 1 = 3 – 1 = 2

largest – smallest = count – 1 , therefore, the series is sequential

e.g. 4

243, 246, 244, 245, 242, 247

largest = 247

smallest = 242

largest – smallest =247 – 242 = 5

count – 1 = 6 – 1 = 5

largest – smallest = count – 1 , therefore, the series is sequential

Neat, huh?

Don 7, Mice 2

The final tally of mouse casualties was seven.  I’ve not seen any sign of mice in about a month, despite having left out bait.

I’ve upped the casualty count on my side because, after Halloween, I discovered more candies which the mice had attacked…candies which I inadvertently gave to an unsuspecting trick-or-treater!

It is possible that the casualty count on the side of the mice is actually higher if one considers the possibility of one or more mice having succumbed, in hiding, to the poisoned food I left out for them (and from which they heartily ate).

Peace at last…but, for how long?