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Hint needed. The cells marked with dots must be white.enter image description here

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  • $\begingroup$ Do you have a source for this puzzle? Also, the rules may be found here (en.wikipedia.org/wiki/Heyawake) for this type of puzzle. Also also, why did you mark some squares with dots? $\endgroup$ – Brandon_J Jan 12 at 20:55
  • $\begingroup$ I can confirm that op is correct so far. One option is to deduce based on there being a unique solution that the 2nd row 4th from the left is colored in. If it were not then the top middle one of that room could go either way... $\endgroup$ – Dr Xorile Jan 12 at 20:58
  • $\begingroup$ This puzzle is from the book amazon.com/gp/product/1783351365 $\endgroup$ – George Dontas Jan 13 at 10:17
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You can make a series of deductions marked as red, yellow, green, blue, and purple

puzzle solution

The logic here is as follows:

Red: you can't have an uncolored orthogonal line for more than 2 rooms, so this must be colored.

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Yellow: forced because of the 3 in that room and the red. (OP already figured out that the three is necessary because of the empty rooms on either side.)

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Green: needed because otherwise there would be three rooms.

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Blue: 3 rooms

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Purple: 3 rooms.

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