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In these puzzles, the goal is to fill every empty square (including shaded squares) so that:

1. Each square contains a positive digit (1-9). Digits may be reused.

2. The percent next to a row gives the percent of the row sum contained in the shaded square of that row.

3. The percent above each column gives the percent of the column sum contained in the shaded square of that column.

 

 Jun 21, 2021
 #1
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33 1/3% is equivlent to 1/3, 40% is 2/5, 75% is 3/4, and 50% is 1/2.  

 

Let's look at the top left black square, with the number in it equal to x.

 

Because the number above it is 1/3, we know that it is 1/3 of the column, so the white square below it is 2/3.  In this, we know that the bottom left white square is 2x.  

 

Moreover, because the bottom right black square is 25% of the bottom row, we have 2x as 75% of the bottom row.  

 

This means that the entire bottom row sums to 8/3x, and the black bottom square is 2/3x.  

 

With 2/3x being 50% of the right column, the white square is also 2/3x.  

 

Knowing this, we know that x is divisible by 3, and that 8/3x < 10.  This means that x must equal 3.  

 

However, plugging this value into the puzzle, we find that this is impossible.  Thus, there is no solution.  

 

Intuitively, we see that the top right square must be less than 5, meaning that the values are either 1, 2, 3, or 4 (or else the square under it will be greater than 10).  With each of these values, however, there is no solution.  

 Jun 21, 2021

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