1. The problem statement, all variables and given/known data There are patterns made up of square tiles which I can not draw but only describe... Pattern 1 has 1 grey tile in centre and 8 dotted tiles around it Pattern 2 has 4 grey tiles in centre and 12 dotted tiles aound it Pattern 3 has 9 grey tiles in centre and 16 dotted tiles around it Pattern 4 has 16 grey tiles in centre and 20 dotted tiles around it and so on 2. Relevant equations So the table looks like this Pattern number 1, 2, 3, 4, ... Number of grey tiles 1, 4, 9, 16, ... Number of dotted tiles 8, 12, 16, 20, ... 3. Work out what the total number of tiles there are in pattern 11 So I got for number of grey tiles pattern number 11 squared = 121 and nth term for the number of dotted tiles is 4n+4 so for n=11 we get 48 Hence total number of tiles is 121+48= 169 4. What is the number of the pattern in which the total number of tiles is equal to tsquared? As the grey tiles are already equal to tsquared for any pattern number t, so any additional tiles e.g. any dotted tiles would just add more to tsquared. So, the only number of the pattern in which the total number of tiles is equal to tsquared must be pattern 0 (zero). Am I correct? If not, explain why? Is this correct?