Problem Of the Week: 29th January 2024
One of the CCF's guns is designed such that it can launch a projectile of mass 10 kg at a speed of 200 m/s. The gun is placed close to a straight, horizontal railway line and aligned such that the projectile will land further down the line. A small rail car of mass 200 kg travelling at a speed of 10
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Problem Of the week: 29th January 2024
Michael Wu
An unreliable typist is trying to type 'Eton College' into their Chronicle article, but cannot guarantee that the order of the letters are correct. Thus he may type 'Eetgne ooCll' or 'egelloC ontE'. How many possible outcomes are there for this typist? Hint Think about how duplicates of letters may affect the answer. Also note the space and that capital letters are different to their lower case equivalents. Solution We can look at this problem chronologically, how many possible options does the typist have for the first character? There are 12 options in ‘Eton College’, so there are 12 options for the first character. Now we look at the second character, since we have already chosen an option for the first character, there are only 11 options. This pattern continues for the entire phrase, and can be summed up with a factoral (those unfamiliar with this term: 6! = 6x5x4x3x2x1): 12! However, we have not accounted for any duplicate solutions; as there are 3 letters which are repeated once (e, o, l). Therefore we must divide by 2! three times, leaving us with the following as the solution: 12!/ 2! x 2! x 2! = 59,875,200.
