Name: Vanessa

Who is asking: Student
Level: Secondary

Question: I have a math puzzle. I have been working on it for over 2 weeks. Here it is: use the numbers 1-25 each only once. The rows across are an equation and the columns down are an equation. There are 25 boxes. You have to use the order of operation x and / first then = and -. Some of the answers are -numbers.

nxn-n-n+n=89
x   -   -   -   +    
n-nxn+n/n=-55
+   +   x   +   +    
n-nxn-n-n=-116
/ x - + +  
n+n+n-n/n=34
+ + - x +  
n+nxn+n+n=256
=      =      =      =      =       
126      131      -130      192      49       

b= Blank These were black squares on the puzzle.

The rows and columns have to equal the answer across and down. I tried to do the -numbers first. I then tries to work backwards from the answer. I tried factoring the number and using the answers. I got 7 of the equations done and the remainng numbers wont work. I would apreciate any help I can get. All this work for 10 POINTS. I would rather write a paper on a great mathamatician.

Thanks
Vanessa

Hi Vanessa,

We would also rather write a paper on a great mathematician. There seems to be no way to get around checking zillions of possibilities.

On the other hand, puzzles like that one are easy to invent: Just write down the numbers from 1 to 25 in a table in any order:

7   23   18   9   25       
                     
8   11   6   3   17    
                     
4   19   20   10   14    
                     
15   13   2   16   22    
                     
5   1   21   24   12    
                                             

Then put in division signs first, where they fit, and fill up the rest with other operations:

7 + 23 - 18 / 9 + 25       
-   x   /   x   +    
8 + 11 x 6 + 3 - 17    
/   -   -   +   x    
4 x 19 + 20 / 10 + 14    
+   -   +   x   -    
15 - 13 + 2 x 16 - 22    
x   /   x   -   -    
5 x 1 + 21 - 24 / 12    
                                             

Then solve the operations on rows and columns and hide the numbers:

7 + 23 - 18 / 9 + 25 = 53
-   x   /   x   +    
8 + 11 x 6 + 3 - 17 = 60
/   -   -   +   x    
4 x 19 + 20 / 10 + 14 = 64
+   -   +   x   -    
15 - 13 + 2 x 16 - 22 = 22
x   /   x   -   -    
5 x 1 + 21 - 24 / 12 = 24
=      =      =      =      =       
80        221        25        163        229        

Voila! you have a puzzle as tough as the previous one, and you can throw it back at whoever assigned that monstrosity.

Claude
Go to Math Central