“Cruel” Sequences Puzzle

Here’s a fun math treat, a great puzzle to pose when you have just a few minutes of class left. It’s guaranteed to drive your students “to distraction.”

As we know, one important area of math involves the study of sequences — those strings of numbers or terms that have some order to them. Often your task in studying sequences is to figure out the next number or term in the sequence — or to figure out the pattern on which the sequence is based.

Here’s a simple example. What would be the next number in this sequence: 

1, 4, 9, 16, 25, ?

The answer is 36, since the elements of this sequence are simply the perfect squares of the natural numbers.

Algebra, as we know, involves using letters in place of numbers, so what better time to introduce a sequence involving letters.

Ask someone if s/he can figure out the next letter in this sequence:

O, T, T, F, F, S, S …

Kids will puzzle over this agonizingly. But the answer is remarkably simple. The answer is E.

The reason:  the sequence of letters are the first letters of the first numbers in the Natural Numbers:  One, Two, Three, Four, Five, Six, Seven. The next number is Eight, so the next letter is E. Isn’t that just cruel?

Supposedly, as the story goes, this problem was given both to MIT graduate students and second graders. Guess who got it faster? The second graders.

If there is a moral to the story, it may just be that sometimes we over-think situations. It’s important to keep in mind that the answer may be right in front of our noses.


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One Response to ““Cruel” Sequences Puzzle”

  1. Jill Brouillard says:

    Along the same lines. . .

    8, 5, 4, 9, 1, 7, 6, 3, 2, 0

    Find the pattern/ order of these numbers. The answer is down below . . .
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    It’s the digits 0 through 9 in alphabetical order

    #