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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.
Solve this puzzle for yourself at the same time.
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Step 2
The only way to make 12 in two squares using multiplication is 3 x 4.
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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).
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Step 4
The only way to make 7 in three squares using addition is 1 + 2 + 4.
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Step 5
As we know where the <1>, <2> and <4> of Row 1 are, we know that this square is <3>.
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Step 6
As this cage must equal 2 under subtraction, it must be 3 - 1, which makes this square <1>.
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Step 7
Neither of these squares can contain <4>. This is because the 12x clue in this column MUST contain the <4>.
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Step 8
Removing <4> on the previous step forced the <1> of this cage, which makes this square the <4>.
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Step 9
As we now know where the <1> for this column is, we can remove it from this square leaving the <2>.
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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>.
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Step 11
Row 1 is only missing its <4>, and that must go in this square.
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Step 12
This square can only be <2> as the other numbers are either in Row 4 or Column 4.
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Step 13
Both of these numbers are forced as each only has one number left in the Row or Column.
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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>.
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Step 15
This square can only be <2> as all other numbers already occur in the row or column.
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Step 16
These squares are now forced as each only has one number left in the row or column.
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Step 17
There is only one number that this square can be, and the puzzle completes.
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Step 18
The completed puzzle.
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