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How many such pairs of letters are there in the word FOREIGN, each of which has as many letters between them in the word as in the English alphabetical series?

Question

How many such pairs of letters are there in the word FOREIGN, each of which has as many letters between them in the word as in the English alphabetical series?

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Solution

To solve this problem, we need to look at the word FOREIGN and the English alphabetical series (A-Z) and find pairs of letters that have the same number of letters between them in both.

  1. Start by writing down the word FOREIGN and the English alphabetical series.

  2. Look at each pair of letters in the word FOREIGN and count the number of letters between them.

  3. Then look at the same pair of letters in the English alphabetical series and count the number of letters between them.

  4. If the number of letters between the pair in the word FOREIGN and the English alphabetical series is the same, then it is a valid pair.

  5. Repeat this process for all pairs of letters in the word FOREIGN.

  6. The total number of valid pairs is the answer to the problem.

Let's do this step by step:

  • The pairs in FOREIGN are (F,O), (F,R), (F,E), (F,I), (F,G), (F,N), (O,R), (O,E), (O,I), (O,G), (O,N), (R,E), (R,I), (R,G), (R,N), (E,I), (E,G), (E,N), (I,G), (I,N), (G,N).

  • The pairs that have the same number of letters between them in the word FOREIGN and the English alphabetical series are (F,O), (O,R), (R,E), (E,I), (I,N).

So, there are 5 such pairs of letters in the word FOREIGN.

This problem has been solved

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