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The seventh pattern will be a 15 x 15 figure.

Total number of tiles: 15 x 15 = 225

No. of black tiles: 15 +15 + 1 + 4 + 4 +4 +4 +4 +4 = 55

* The two 15s are from the left most and right most columns, the 1 is the one right in the centre, the 4s are the additional four tiles spread diagonally outwards  in all four directions from the centre

No. of white tiles: 225 – 55 = 170

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hi! tq for ur help! did u mean that the 7th pattern will be a 15×15 figure?

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Hi yes. Sorry for the typo.

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may I know how did u derive at 15×15 for pattern no.7? 

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Hi, I multiplied the Pattern no. by 2 and added 1 to it. This works for all Patterns numbers except for the first.

The table below should illustrate it better:

Pattern No. No. of tiles (side) No. of tiles (total)
Pattern 3 (3 x 2) + 1 = 7 7 x 7
Pattern 4 (4 x 2) + 1 = 9 9 x 9
Pattern 5 (5 x 2) + 1 = 11 11 x 11
Pattern 6 (6 x 2) + 1 = 13 13 x 13
Pattern 7 (7 x 2) + 1 = 15 15 x 15
Pattern 8 (8 x 2) + 1 = 17 17 x 17
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crystal clear! thanks so much for ur effort in explaining it so simply😊

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