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Mathematics-Online problems:

Interactive Problem 57: Combinatorics of a Letter Rhombus

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The figure shows a rhombus filled with a pattern of letters, that are taken from the words MATHE and ONLINE.

\begin{picture}(12,13) % 10.Zeile \put(6,1){M}\put(5,1){O} % 9.Zeile \put(7,2){M... ...){A}\put(6,9){N} \put(7,9){O} % 1.Zeile \put(5,10){M}\put(6,10){O} \end{picture}

  1. How often can the combination of the words MATHE and ONLINE be read in the pattern, if both horizontal and vertical combinations of letters were allowed?

  2. How many possibilities exist, if the letter E in MATHE were to coincide with the E in ONLINE?


Answer:

  1.
  2.


   

(From: Day of Mathematics 1994)
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  automatically generated: 8/11/2017