# Java, <s>257</s> <s>246</s> 210 bytes

```
a->{Integer r=9,i=512,j,x,y,k,p,z;l:for(;i-->0;){for(p=j=-1;++j<3;){x=y=0;for(k=9;k-->0;x+=k/3==j?z:0,y+=k%3==j?z:0)z=(i&1<<k)>0?7:a[k];p=p<0?x:p;if(x!=p|y!=p)continue l;}r=Math.min(r,r.bitCount(i));}return r;}
```

*Saved 11 bytes thanks to [ceilingcat](https://codegolf.stackexchange.com/users/52904).*

*Saved 36 bytes thanks to [Olivier Grégoire](https://codegolf.stackexchange.com/users/16236).*

Takes a flat array as input. This method tries all 512 (2<sup>9</sup>) possibilities by using the binary representations of the integers from `0` to `511`. On each iteration, it sets the values at all indexes where `i` has a set bit to `7`. Then, it checks if the current array is valid, in which case the answer is updated.

[Try it online!](https://tio.run/##TVLBjpswEL3nK9xDK1AGCgG2CcaJVpUq9bCn7S3KwZuFrYEYZEwESfn2dOySqBrZnnnzZjx@UPIz98r36nasedeRl@uCtP1bLY6k01zjcW7EOzlxIYnzqpWQH/vDs4ssUmKl32tR@0Uvj1o00v/V/JT6xxxl6OcfudoftqQg7Ma97XWGiGIbECwJV1DCACNU0MKF1mnRKIcKz9sG1L2aoGUl80K6XJZZhNDARhZQk6jYhlaWOCxZ9TVirNxd0gBGjD7fI/fCHPElzLLK3Qa7bynfVwfasjYLdkPaUlE4wyfW/hlxc4@N1EL2OanppNgL17/9k5COAuW/Cf296aV2hOtiMte9kkTR6UZRhscr9wedd7pjRhty3UAMEVoMxltDPIHFEwgtHoLxVhDOeIS8J@QlaMiG4MGPLHMDia2LZnyNfoDM@7r3N31XuAz/ydQ8@htWaNlmgvUDN5l/NxhLZnyFMyT2ztja@r8@WG2nMns8ITwZIcxXOXNFjAqplcIlr2On85Pf9Npv8d/RtXQKn7dtPT53KJxjaKjpgkyL6fYX)