Fill in each of the ten labeled boxes in the grid below with a different digit from 0 to 9 to form eight two- and three-digit numbers in the rows and columns (four reading across and four reading down).   Can you find a way to fill the grid so that the following statements are true?

  1. Each digit from 0 to 9 is used once.
  2. No number begins with 0.
  3. Seven of the eight numbers are prime; the number that is not prime reads across.
  4. One of the prime numbers is the sum of two others.

         
  		         
  		         
  		         
  		  J      
 
         
  		         
  		         
  		  H      
  		  I      
 
         
  		         
  		  F      
  		  G      
  		         
 
         
  		  C      
  		  D      
  		  E      
  		         
 
  A      
  		  B      
  		         
  		         
  		         
 


Please send in you answer in the following format:
A =
B =
C =
D =
E =
F =
G =
H =
I =
J =


 

Solution to the Problem:

         
  		         
  		         
  		         
  		  5      
 
         
  		         
  		         
  		  4      
  		  3      
 
         
  		         
  		  6      
  		  0      
  		         
 
         
  		  2      
  		  7      
  		  1      
  		         
 
  8      
  		  9      
  		         
  		         
  		         
 

To solve the puzzle, first determine where 0 must be.
Clue #2 states that no number begins with 0, so 0 must be in boxes B, D, E, G, or I.
Clue #3 states that there is only one number that is not prime.
    Hence, 0 must be in box D or box G or else there would be two numbers that are not prime.
Clue #3 also states that the non-prime number reads across, so 0 must be in box G.

Now continue to solve, making use of the following facts:
B, D, E, and I must be odd numbers (evens would create more numbers that are not prime).
The number 5 can not be placed in these boxes because it would create another non-prime number.
Hence, boxes B, D, E, and I must contain 1, 3, 7, and 9 (not in that order).
Clue #4 tells us that one prime number is the sum of two other numbers. The other two numbers can not both be prime because the sum of two numbers ending in an odd digit would be even and therefore, not prime. So, the number located in boxes F and G must be added to one of the primes to form a larger prime. Since the composite number ends in zero, you need two primes that end in the same odd digit.
60 + 29 = 89.



Correctly solved by:

1. David & Judy Dixon Bennettsville, South Carolina
2. Elvis Nguyen Lakeridge High School
Lake Oswego, Oregon
3. Sagar Patel Brookstone School
Columbus, Georgia
4. Tristan Collins Virginia Tech
Blacksburg, Virginia
5. Kunal Singh Kendriya Vidyalaya
Happy Valley, Shillong, India
6. Magdy Essafty Alexandria, Egypt
7. Cynthia, Steve, and Leonard Manual Arts High
Los Angeles, California
8. Andrew Dau South O'Brien High School
Gaza, Iowa
9. Danny Gordon Brookstone School
Columbus, Georgia
10. Britney White Brookstone School
Columbus, Georgia
11. Sharina Smith Newport News, Virginia
12. Garrett Hix Brookstone School
Columbus, Georgia
13. Yassee Pirooz Harrisonburg High School
Harrisonburg, Virginia
14. Laura Gronauer John Handley High School
Winchester, Virginia
15. Julianne Harris John Handley High School
Winchester, Virginia
16. Maggie Morrison John Handley High School
Winchester, Virginia
17. Amanda Corsnitz John Handley High School
Winchester, Virginia
18. Matt Ahrnsbrak John Handley High School
Winchester, Virginia
19. Kelley Kolar John Handley High School
Winchester, Virginia