Number Grids
Instructions: Draw a 3x3 grid. Then 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 in each puzzle. There are hints below and solutions below that.
Puzzle #1
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.
Puzzle #2
The number in the lower left corner is the sum of the numbers in all the other corners.
There is a column with a sum of 10.
No even number is immediately to the left of another even number.
One row has a product of 30.
There is a row with a sum of 21.
No odd number is immediately below another odd number.
Puzzle #3
There is a row, column, or diagonal in which the sum and the product are equal.
4 is between 2 and 5 on a straight line.
6 does not share a row, column, or long diagonal with 7.
3 is between 4 and 8 on a straight line.
The sum of one of the long diagonals is odd.
There is a number in the left-hand column that is 3 times the number in the lower right corner.
Puzzle #4
3 does not share a row, column, or long diagonal with 1 or 4.
The bottom row has a sum of 20.
The column on the right has a sum of 7.
There is a row which contains only prime numbers.
The column on the left has a sum of 16.
Puzzle #5
There is a long diagonal with a sum of 9.
The 3 is some distance above the 9 in the same column.
The 4 does not share a column or row with the 2 or the 3.
There is a long diagonal with a sum of 22.
The 9 is some distance to the right of the 7 on the same row.
Puzzle #6
All rows have the same sum.
The number in the lower left corner is the product of the numbers in all the other corners.
Any numbers spelled with the same first letter are in the same column.
The 5 does not share a row or column with the 8.
Puzzle #7
Both long diagonals have even sums.
2 is between 9 and 5 on a straight line.
5 is between 8 and 3 on a straight line.
1 does not share a row or column with 4.
The number in the upper right corner is the sum of the other two numbers in its row, its column, and in its diagonal.
The sum of the bottom row is odd.
Puzzle #8
The sum of the numbers in the four outer corners is 12.
6 does not share a row with 7. (7 ate 9, you know.)
The numbers in the bottom row are in increasing order from left to right.
Both long diagonals have odd sums.
The product of the numbers in the left column is 35.
Puzzle #9
The 8 is between the 1 and the 5 on a straight line.
There is a number in a corner that is the sum of the other two numbers in its row, column, and diagonal.
The numbers in the left column have an odd product.
No odd number is to the immediate left of another odd number.
The 2 is immediately below the 5.
Puzzle #10
There is a row with a product of 12.
The number in the upper right corner is the sum of the numbers in all the other corners.
All columns are in descending numerical order from top to bottom.
Both long diagonals have an odd product.
SPOILER ALERT! HINTS BELOW!
Hints
Puzzle #1
First look at the 4th rule, then the 1st rule.
Puzzle #2
Use the the 3rd and 6th rules together. (Try putting an even number in the upper left hand spot and see what happens.)
Puzzle #3
First, look at the 2nd rule, then the 4th , then the 1st.
Puzzle #4
Look at the 3rd rule, then the 2nd. For more help, look at the 5th, then 1st.
Puzzle #5
First, look at the 4th rule, then the 5th , then the 2nd.
Puzzle #6
Use the 1st rule first. (what does the sum have to be?) then the 2nd rule.
Puzzle #7
Look at the 2nd rule, then 3rd, then 1st.
Puzzle #8
Look at the 5th rule, then the 1st, then the 3rd.
Puzzle #9
Look at the 3rd rule, then 4th, then 2nd.
Puzzle #10
Look at the 4th rule, then the 2nd rule.
SPOILER ALERT! SOLUTIONS BELOW!
Solutions
Puzzle #1
562
943
871
Puzzle #2
523
876
941
Puzzle #3
187
639
542
Puzzle #4
681
352
794
Puzzle #5
823
456
179
Puzzle #6
294
375
861
Puzzle #7
178
925
643
Puzzle #8
562
789
134
Puzzle #9
185
962
347
Puzzle #10
589
276
143