Find the square that can only be one number
A calcudoku tray is solved one square at a time. Look for the square that can only be one number, and the rest follows.
A cage of one square is already that number, so fill every one of them first.
A cage of two squares marked 2 divide on a 4 by 4 tray holds 1 and 2, or 2 and 4. Nothing else divides to 2.
Every row adds to the same total: 10 on a 4 by 4 tray, 15 on a 5 by 5, 21 on a 6 by 6. So a cage that fills most of one row gives away the square it leaves.
One 4 by 4 tray, square by square
Here is the whole tray, in the order the squares fall. Rows are counted from the top and columns from the left.
- Row 4, column 1 is a cage of one square, so it is 2.
- Row 1 adds to 10, and the 6 plus cage fills three of its squares. So row 1, column 4 is 10 take away 6, which is 4.
- The 2 divide cage holds that 4 and the square under it. 4 divided by 2 is 2, so row 2, column 4 is 2.
- Column 1 already has the 2 at the bottom. The 1 take away cage holds its two middle squares, and the only pair one apart left is 3 and 4. So row 1, column 1 is 1.
- The 3 take away cage in row 2 needs 1 and 4. Row 2 cannot hold two 4s, so row 2, column 1 is 3.
- The 1 take away cage is 3 and 4, and the 3 is above, so row 3, column 1 is 4.
- The 3 divide cage takes 1 and 3 in column 2, so the 1 of the 3 take away cage cannot sit there. Row 2, column 2 is 4.
- The 3 take away cage is 1 and 4, and the 4 is beside it, so row 2, column 3 is 1.
- Column 2 now has that 4, and the 3 divide cage takes 1 and 3, so row 1, column 2 is 2.
- Row 1 has 1, 2 and 4, so row 1, column 3 is 3.
- Column 3 has 3 and 1. The 2 times cage can only be 1 and 2, so row 3, column 3 is 2.
- The 2 times cage is 2 and 1, so row 3, column 4 is 1.
- Column 3 has 3, 1 and 2, so row 4, column 3 is 4.
- The 12 times cage is 4 and 3, and the 4 is beside it, so row 4, column 4 is 3.
- Row 3 has 4, 2 and 1, so row 3, column 2 is 3.
- The 3 divide cage is 3 and 1, and the 3 is above, so row 4, column 2 is 1.
Which square can you fill first?
A fresh 4 by 4 tray has a cage marked 9 plus across the first three squares of the top row.
Nothing else on the tray is filled in. A 4 by 4 row adds to 10, so one square in that row can be worked out straight away.
Try it
Which square of that top row can you fill straight away?
- The fourth square, the one outside the cage
- The first square, at the left of the cage
Show the answer
The fourth square, the one outside the cage
Correct. The row adds to 10 and the cage takes 9 of it, so the square outside the cage is 1.
Enable JavaScript to answer interactively and save your place.
Practice Calcudoku