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Investigation 'Tiles' A builder is asked to arrange some tiles on a wall in a 4 by 4 array as shown below To help him he has variously shaped 'spacers' which he places between the tiles. He uses the spacers to separate the tiles evenly as in the following arrangement. He has used 4 spacers like this He uses 9 spacers shaped like this He uses 12 spacers shaped like this He has 25 spacers altogether Aim of Investigation: The aim of this investigation is to investigate the number of different types of spacers required for other arrangements of tiles. Result Table 1: Arrangement (A) C S N 1 by 1 4 0 0 2 by 2 4 1 4 3 by 3 4 4 8 4 by 4 4 9 12 By observing the results from this table after drawing the arrangements, as shown above, I have discovered a formulae using the trial and error method to find out what spacers I need for the different arrangements. Formulae C= 4 S = (A - 1) 2 N = 4(A - 1) I have also discovered...

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