The Top?

Logic Level 2

This is a calcdoku puzzle where each coloured box is a section.

If there is a solution what is the 4 numbers (left to right) from the top row.


The answer is 1324.

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1 solution

Douglas Foster
Dec 16, 2019

Starting with the green box: The only three numbers that work are 1+1+3, (EDIT: due to the restriction from the brown box, which must be 2 and 4 in some order), and since you cant have two 1's in the same row the you have 1 and 3 in the top row and 1 in the last empty space for the green box.

Then the first column is down to having 2, 3, and 4, which multiply to 24, so the last space in yellow box must be a 2.

Then column 2 will have a 1, 2, and 3 so the empty box in column two (column 2 row 3, grey box) will be a 4. So the rest of grey box multiplies to 6, which is 1x2x3.

Since the 1 in row 2 column 2 cancels out the top two grey boxes and you know that row 3 column 3 is the 1.

The 3 1's down the diagonal only leave row 4 column 4 open for the last 1. So the two empty spots in blue must be 3+4 to get the total up to 8.

The 4 in row 3 column 2 means the blue box 4 must go in row 4 column 3. This forces the 4 in row 1 to go in column 4 and the 2 in row 1 to go in column 3.

That fills the top row with 1324.

You can complete the puzzle easily from here but it is not necessary to get the correct solution.

The green box could also be 2+2+1

Emily Peng - 1 year, 5 months ago

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edited my solution to include the restriction from the brown box being 2 and 4 that makes green 1,1,3

Douglas Foster - 1 year, 5 months ago

I believe this does not actually have a solution. As the top right box is 8x, the top left box must be 1,3, and 1 (on the row below). 48 can be decomposed as 48 = 4x4x3x1 = 4x3x2x2. Notice that there are 1s in both the 1st and 2nd columns already. Thus, we must us the form 48=4x3x2x2 with the 2s in the top left and bottom right squares of this box. Notice now that the second column is (in decending order) 31?2. The ? must be a 4. Now decompose 24=4x3x2x1. We must use this decomposition as there is 4 in a square in this bow. We must put a 1 next to the 4 as there is a 1 blocking the above row. But wait, we now have to put a 2 in a row where there is already one. Thus, this calcdoku does not have a solution.

Louis Schatzki - 1 year ago

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"with the 2s in the top left and bottom right squares of this box" - this isn't true, the two can go in either the top left or second from top left. If you choose second from top left then the rest works. (the other 2 does have to go bottom right as you noted. final solution is 1324 4132 2413 3241

Douglas Foster - 6 months, 1 week ago

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