ҹ1000

Solution to Enigma No. 1608

11 August 2010

Answer: 1 and 7       

The winner Isabel Currie of Caversham, Reading, UK.

Worked solution

The full picture is:      

MISSING GRAPHIC       

212221

2131222

13233311

1321232

213211

The start of one possible approach:    

We can gradually build up the picture to get this answer.

Let (a,b) denotes the bth cell in row a.

Then (for example) if (4,2) had honey then (4,1) and (5,2) would already be satistfied, meaning that (3,1), (3,2), (4,3), (5,1) and (5,3) would be empty. Then the ‘3′ in (4,2) would tell you that (3,3), (4,1) and (5,2) had honey. But then (5,1) has 3 honeyed neighbours, which is not allowed. Therefore (4,2) does not have honey.

Therefore ‘2′ in (5,1) shows that (4,1) and (5,2) have honey.

So the ‘1′ in (3,1) is satisfied and (2,1) and (3,2) do not have honey.

We can continue in this way to uniquely build up the whole picture as above.

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