BOSS agent F6exb used Excel as a tool to find the solution this week and was first to crack the puzzle. This is how they did it:
Hello Harry and Elves,
I apologize for my bad english but I think you can understand what I mean.
You asked me to write how I used Excel to solve puzzle #2.
Excel only helped me to automate the calculations and do the job without
an eraser and pencil.
[Denis made an Excel(lent) spreadsheet with five rows and five columns. The top row computed the columns sums and the last row computed
the column products.
The first column computed the row sums and the last column computed the row products. Harry]
And now, how I did it :
No even number is immediately to the left of another even number.
No odd number is immediately below another odd number.
===> odd and even number alternate.
From 1 to 9 there are 5 odd numbers and 4 even numbers.
So the square begins with an odd number, and every corner plus center
In the lower left corner, I wrote the formula to add the 3 other
corners, but I know that it is 9, and 7 can’t be in a corner. So 7 is in
the center square.
There is a column with a sum of 10.
It is not the first column because of the 9, nor the second because of
the 7. So it is the last column.
One row has a product of 30.
30 = 2 * 3 * 5 or 30 = 1 * 5 * 6. It is the first row.
There is a row with a sum of 21.
It is the second or last one.
With a 9 in the lower left corner, we need 9 + 7 +5 or 9 + 6 + 6, it is
7 is already in the center square so it is the second row. We need 14
more so we have 8 and 6 in this row.
To have 10 in the last column we must have the 6 on the right of the 7.
One row has a product of 30. (Again)
30 = 2 * 3 * 5 or 30 = 1 * 5 * 6. It is the first row. But with the 6 in
the second row, the first row is 2 * 3 * 5.
Now it is quite finished. 4 is in the middle of the last row and with a
little cut and try with Excel, it is done.
Arrange the numbers 1 through 9 in the grid so that all of the conditions in the puzzle are satisfied. Every number is used once. The rules are
- The number in the lower left corner is 4 times the number in the upper right corner.
- The 9 is between the 5 and the 8. (on a straight line)
- There is a column in which the sum is equal to the product.
- The 4 is between the 9 and the 3. (on a straight line)
- No prime number is immediately to the left of a prime number.