# The Vacuumed Quotes

A colleague of mine likes to put his favorite quotes up on the fridge using those little magnetic letters. This morning the cleaner came and accidentally vacuumed up all the letters. We were able to retrieve all the letters (100 in total), but unfortunately we can't remember any of the quotes. Can you help us putting them back up before my colleague returns?

Fortunately, the contours of the quotes are still there, i.e., the number of letters for each word are known. Also, my colleague has the habit of adding a weight to each word, which is built up as follows: the weight of a word is the sum of the weights of its letters and those are given by A = $1$, B = $\frac{1}{2}$, C = $\frac{1}{3}$, ... , Z = $\frac{1}{26}$.

E.g.:

$$it \implies \frac{1}{9} + \frac{1}{20} = \frac{29}{180}$$

$$is \implies \frac{1}{9} + \frac{1}{19} = \frac{28}{171}$$

$$easy \implies \frac{1}{5} + 1 + \frac{1}{19} + \frac{1}{25} = \frac{3070}{2375} = \frac{614}{475}$$

The weight of each word is always given as the most simplified fraction.

Below is the basic lay-out of the fridge at the moment. Beneath each quote the weight of the individual words are given.

## Quote 1

$$\begin{array}{cccccc}\textbf{ _ _ _ }&\textbf{ _ _ _ }&\textbf{ _ _ _ _ _ }&\textbf{ _ _ }&\textbf{ _ _ _ _ }&\textbf{ _ _ _ }\\(\frac{363}{325})&(\frac{3}{8})&(\frac{37}{45})&(\frac{7}{10})&(\frac{2729}{8280})&(\frac{27}{175})\end{array}$$

## Quote 2

$$\begin{array}{cccc}\textbf{ _ _ _ _ }&\textbf{ _ _ }&\textbf{ _ _ _ }&\textbf{ _ _ _ _ _ }\\(\frac{15091}{52440})&(\frac{18}{65})&(\frac{3}{8})&(\frac{6211}{13650})\end{array}$$

## Quote 3

$$\begin{array}{cccccc}\textbf{ _ _ _ }&\textbf{ _ _ _ _ _ }&\textbf{ _ _ }&\textbf{ _ _ }&\textbf{ _ _ _ _ _ _ }&\textbf{ _ _ _ _ _ _ }\\(\frac{519}{475})&(\frac{67}{120})&(\frac{7}{60})&(\frac{38}{325})&(\frac{26}{45})&(\frac{359}{420})\end{array}$$

## Quote 4

$$\begin{array}{ccccccc}\textbf{ _ _ _ }&\textbf{ _ _ _ _ }&\textbf{ _ _ _ _ _ _ }&\textbf{ _ _ }&\textbf{ _ _ _ }&\textbf{ _ _ _ _ }&\textbf{ _ _ _ _ _ }\\(\frac{11}{28})&(\frac{12773}{19950})&(\frac{1567}{2772})&(\frac{11}{90})&(\frac{11}{28})&(\frac{12773}{19950})&(\frac{3877}{6300})\end{array}$$

## Quote 5

$$\begin{array}{cccccc}\textbf{ _ _ _ }&\textbf{ _ _ _ }&\textbf{ _ _ }&\textbf{ _ _ }&\textbf{ _ _ _ _ _ }\\(\frac{27}{175})&(\frac{11}{8})&(\frac{18}{65})&(\frac{21}{20})&(\frac{67}{120})\end{array}$$

And here are the letters that were found in the vacuum cleaner:

4A 3B 1C 3D 13E 2F 4G 7H 6I 7L 5M 4N 9O 3R 4S 9T 4U 1V 2W 9Y


• @Rubio: Thanks for the edit, looks a lot better this way ;) – Levieux Feb 8 '17 at 7:47

• @Matt: No? Prelude Data.Ratio> 1 % 13 + 1 + 1 % 25 == 363 % 325 – Ry- Feb 7 '17 at 14:05