First word on each volume of a dictionarySuppose you have to write a dictionary of a language with 27 letters (Spanish): 5 vowels and 22 consonants (yes, Ñ is included). Each word of this new language is made of two letters one wowel and one consonant. Find what would be the first letter on each volume, knowing that the order is alphabetical and there will be 4 volumes.Knowing how many words there will be in total (220) and in each volume (55) is an easy task, finding the first word of each book seems to be not straightforward (at least to me). I want to know if there is an easy method other than writing the dictionary.

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Daniella Cochran · Accepted Answer

Step 1You have correctly determined that there are 220 words consisting of one vowel and one consonant and that there will be 55 words in each of the four volumes if the number of words in each volume is the same.Observe that each vowel is the first letter of 22 words since there are 22 consonants and that each consonant is the first letter of 5 words since there are 5 vowels.Step 2Clearly, the first volume begins with the word ab, so its first letter is a. To determine the first letter of the second volume, observe that the number of words beginning with the first few letters of the alphabet:                    a                    22                            b                    5                            c                    5                            d                    5                            e                    22            Since   22  +  5  +  5  +  5  =  37  &amp;lt;  55  &amp;lt;  59  =  22  +  5  +  5  +  5  +  22, we may conclude that the first letter of the second volume is e. Moreover, since the last word that ends with e is the 59th word, we know that the first four words of the second volume are ev, ew, ey, ez. That leaves 51 words in the second volume.

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