You have five flavors of ice cream and plan to serve a different one each night for five nights in a row. In what order will you serve them? How many arrangements of five flavors are there, anyway?

The first night, you have five choices. No matter which flavor you pick, the following evening there will only be four choices left, so 5 times 4 equals 20.

The third night, regardless of which two you’ve already dished up, there will only be three flavors left, therefore 5 x 4 x 3 = 60. On the fourth night, only two kinds of ice cream remain, so 60 x 2 = 120. The last night, there is only one flavor in the freezer. One times 120 is, of course, 120. So that’s the number of different ways that five things can be arranged, five at a time.

You are a Broadway composer. To help come up with ideas for melodies, you decide to take the seven notes of the C scale and write out every possible combination using all seven. How many combinations are there?

Using the ice cream logic above, you multiply 7 x 6 x 5 x 4 x 3 x 2 x 1 and come up with 5,040.

Let’s go big. You have a list of 30 words and want to know how many combinations there are using all 30. With the help of a calculator, you figure out that the answer is 2.65e+32 which is scientific notation for 265 followed by 30 zeros. In American English, that is called 265 nonillion. You want to see them, so you tell your computer to list all the 30-word combinations. Even if it spits out a billion combinations a second, there would not be enough time in the entire history of our universe to show all 265 nonillion.

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Here are the 30 words, listed alphabetically. (The word “and” appears twice. Treat it as two separate words.) Read the list and see if you can eliminate all 265 nonillion combinations, except for one that many Americans are familiar with.

a ago all and and are brought conceived continent created dedicated equal fathers forth four in liberty men nation new on our proposition score seven that the this to years

Here is the combination you are looking for:

Four score and seven years ago our fathers brought forth on this continent, a new nation, conceived in liberty, and dedicated to the proposition that all men are created equal.

In addition to those 30 words, Abraham Lincoln added just 241 more to create the Gettysburg Address.

His words were not the only ones delivered from the podium on November 19, 1863, in Gettysburg, Pennsylvania. Before the president delivered his tiny, but brilliant speech, a reverend named Stockton opened the service with a 934-word prayer that few, but God, now remember.

Also, a fellow named Edward Everett spoke for two hours, giving a 13,607-word oration. It must have seemed like a nonillion.

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