A problem for Susan Quek
Level
pending
How many letters are there in the word 'Susan'?
The answer is 5.
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Firstly, we must define 'letter'. It is 'a character representing one or more of the sounds used in speech; any of the symbols of an alphabet.' (from the dictionary) Secondly, we must note that all the characters in the word 'Susan' are used in pronouncing the word.
Lemma 1. The number of letters is equal to the number of characters.
Now we proceed to count the number of characters. We need to tally up the number of times each letter occurs. S: twice U: once A: once N: once In total, there are 2+1+1+1 characters.
Finally, we proceed to the last step: finding 2+1+1+1.
Lemma 2. 1+1=2. This can be proven by taking an apple, taking another one and counting the total number of apples. Since 1 apple + 1 apple = 2 apples and apple is not equal to 0, we can factor out apple and divide it to get lemma 2.
So 2+1+1+1=2+2+1 by substitution. By multiplying the equation 1+1=2 by 2, we get 2+2=4. Thus the number of characters is reduced to 4+1. Now let's say we have 4 apples. Then we add one. Split up the apples so that they stand alone. Now try grouping them into groups of 2 or 3. Then there will be a remainder and there will be no more than 3 groups or 2 groups respectively. However, it cannot be greater than 7 as 2 times 3 is less than 7. Thus 4+1=5 and we are done using Lemma 1.