
Step 1 This is the start of the puzzle. This puzzle has a number of different solution methods, see if you can find another way of solving it.


Step 2 The only way to make 12 in two squares using multiplication is 3 x 4.


Step 3 The only way to make 4 in two squares using multiplication is 1 x 4 (as we can't have two 2's in the row).


Step 4 The only way to make 7 in three squares using addition is 1 + 2 + 4.


Step 5 As we know where the <1>, <2> and <4> of Row 1 are, we know that this square is <3>.


Step 6 As this cage must equal 2 under subtraction, it must be 3  1, which makes this square <1>.


Step 7 Neither of these squares can contain <4>. This is because the 12x clue in this column MUST contain the <4>.
Can you see an alternative solution method that involves the 9+ cage and the missing numbers from Column 4 (that add to 6)?


Step 8 Removing <4> on the previous step forced the <1> of this cage, which makes this square the <4>.


Step 9 As we now know where the <1> for this column is, we can remove it from this square leaving the <2>.


Step 10 As we now know where the <2> from Row 1 and the <4> for Column 1 are we can remove both of these from this square leaving <1>.


Step 11 Row 1 is only missing its <4>, and that must go in this square.


Step 12 This square can only be <2> as the other numbers are either in Row 4 or Column 4.


Step 13 Both of these numbers are forced as each only has one number left in the Row or Column.


Step 14 As we know where the <4> for Row 3 is, we can remove it from this leaving the <3>, which forces the remaining square in Column 2 to be <4>.


Step 15 This square can only be <2> as all other numbers already occur in the row or column.


Step 16 These squares are now forced as each only has one number left in the row or column.


Step 17 There is only one number that this square can be, and the puzzle completes.


Step 18 The completed puzzle.
