Two possible rectangle shapes do not mean you are stuck in Kaku. Remember the cells they must cover and solve another corner first. The upper-left 6 on Easy 163 is a good example. Follow the entire board to learn how to keep a useful unresolved candidate.
Rules for this board
Split the board into rectangles without gaps or overlaps. Each rectangle holds one number, equal to its area. Drag between opposite corners to place a piece and tap a manually placed piece to remove it. Count rows from the top and columns from the left.
Easy 163 is a 7x7 board. Watch the upper-left 6 and the board corners.
Hint 1: Place the piece with one shape
The 4 in row five, column two forms a 2x2 across rows five and six, columns one and two.
Other directions for this 4 collide with another number or the board edge. Placing its only shape also reduces the neighbouring 6s' options.
Hint 2: Keep only shapes that cover the corner
Only the 6 in row two, column one can cover the top-left corner. A 2x3 and a 3x2 shape can still do it.
After placing the 4, this 6 has three candidates. The 2x3 starting in row two leaves the top-left corner empty, and no other number can fill it. Remove that candidate. The 2x3 and 3x2 starting at the top are both still possible, so do not place either yet.
TipKnowing which number covers a cell is different from knowing its full rectangle. Keep both candidates and move elsewhere.
Hint 3: Solve the other three corners
The top-right corner takes a 2x2 for 4, the bottom-left a horizontal 2, and the bottom-right a vertical 3.
For each corner, find the number that can reach it and count that number's shapes covering the corner. Each of these three corners has one remaining shape. You can place all three without guessing the unresolved top-left 6.
Hint 4: Return to the saved candidates
Only the left 6 can cover row one, column three. Its 2x3 shape reaches that cell, so the 3x2 candidate is removed.
The earlier corner restriction now leaves just one shape. Do not forget that restriction and bring back the discarded candidates. After every placement, check the neighbouring numbers again.
Starting with the 8 as a four-row-by-two-column piece, the middle 6s and 4s and the bottom 2 each reduce to one shape.Solved. Keeping the corner restrictions lets us partition the entire Easy 163 board.
Kaku The JoyPlus Soft Planning Team
