What two numbers add up to 9991?

There are infinite combinations of two numbers that add up to 9991. Here are some examples using negative numbers:

-1 + 9992 = 9991
-2 + 9993 = 9991
-3 + 9994 = 9991
...

Here are some examples using two fractions that will add up to 9991:

9991/2 + 9991/2 = 9991
19982/3 + 9991/3 = 9991
29973/4 + 9991/4 = 9991
...

And here are some examples using two decimal numbers that will add up to 9991:

1.25 + 9989.75 = 9991
2.50 + 9988.5 = 9991
3.75 + 9987.25 = 9991
...

As you can see from the lists above, it can go on forever. However, when answering "What two numbers add up to 9991?", it may be more interesting to set some criteria to limit the result. We will set the follow criteria:

1) Only positive whole numbers can add up to 9991. (0 is not a positive or negative number and should not be included.)

2) Since a+b=29 is the same as b+a=29, we should only list it once.

Now, the answer to "What two numbers add up to 9991?" has 4995 answers:

1 + 9990 = 9991
2 + 9989 = 9991
3 + 9988 = 9991
.
.
4993 + 4998 = 9991
4994 + 4997 = 9991
4995 + 4996 = 9991

We have truncated the list above due to space, but you may be interested to know that we calculated the number of answers by dividing 9991 by 2 and then rounded down to the nearest whole number if necessary.

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