Gem Finder: Hidden Gems
Read the puzzle
A 5 by 5 grid; a number counts gems in the 8 tiles around it (diagonals too), numbered tiles hold no gem, and # is a covered tile. Row 1: 0, 0, 1, 1, #. Row 2: 1, B, 2, #, #. Row 3: #, #, A, #, #. Row 4: #, 1, 2, 2, #. Row 5: 0, D, 1, C, 2. A, B, C and D are covered tiles. Which lettered tile hides a gem?
A number counts the gems in the 8 tiles around it; numbered tiles have none. Which lettered tile hides a gem?
Start with the 0s and 1s: they tell you which tiles are empty.
C
The bottom-right 2 touches just two covered tiles, C and its neighbour, so both hide gems. A, B, D are empty.
How to solve it
Start with the zeros, because they clear tiles at once. The 0s in the top-left corner touch B, so B is empty. The 0 in the bottom-left corner touches D, so D is empty too.
Next find a number with no choice left. The 2 in the bottom-right corner touches only three tiles: the 2 above-left of it, the covered tile directly above it, and C. Numbered tiles hold no gems, so the only two places for its 2 gems are C and the tile above it. Both must hide gems, so C has a gem.
Now check A. The 2 in row 4, column 4 touches A, the covered tiles directly above it and to its upper right, the tile to its right (above the corner 2) and C. C and the tile to its right already make its 2 gems, so A and the others around it are empty.
As a final check, the 1 between D and C touches C and nothing else that holds a gem, which agrees.
The usual slip is picking A because it sits in the middle of several 2s. But those 2s are already filled by gems elsewhere.
Takeaway: begin with 0s, then look for a number whose covered neighbours exactly equal its value.
Learn the method: Process of Elimination in Puzzles: Rule Out Until One Is Left
