programming forums Java Mobile Certification Databases Caching Books Engineering Micro Controllers OS Languages Paradigms IDEs Build Tools Frameworks Application Servers Open Source This Site Careers Other Pie Elite all forums
this forum made possible by our volunteer staff, including ...
Marshals:
• Campbell Ritchie
• Jeanne Boyarsky
• Ron McLeod
• Paul Clapham
• Liutauras Vilda
Sheriffs:
• paul wheaton
• Rob Spoor
• Devaka Cooray
Saloon Keepers:
• Stephan van Hulst
• Tim Holloway
• Carey Brown
• Frits Walraven
• Tim Moores
Bartenders:
• Mikalai Zaikin

# Fill in numbers from 1 to 9

Ranch Hand
Posts: 218
• Number of slices to send:
Optional 'thank-you' note:
Fill in numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9 into ..... to make the equations work.
----------------------
- ....(+)....(=).... -
- --- ---------(/) -
- ....(-)....(=).... -
- -------------(=) -
- ....(=)....(*).... -
----------------------

[ March 28, 2006: Message edited by: Rakesh Joshi ]
[ March 28, 2006: Message edited by: Rakesh Joshi ]

Ranch Hand
Posts: 1923
• Number of slices to send:
Optional 'thank-you' note:
I translated this to

Solutions are [71][17]8954632 (a-i).
Most Multiplications get greater than 9 (3*4) so I started there.
1*x is smaller than 10 for every x in (1-9), but would lead to
1*x = x and that's impossible.
h*i=g and i*f=c don't have g or c on the left side.
Therefore h,i,f must be at least 2.
Since 2*5 is 10, every multiplication is too big if a 5(or bigger) and no 1 is involved.
2*3 and 2*4 are the only candidates, which is consistent to our problem: i occures two times and is therefore 2.
h and f are 3 or 4.
Therefore c is 6 or 8 and g is 6 or 8.

If f is 3 or 4, we only have 1,7 and 9 left for d.
But e+f=d, therefore d must be greater than f, which might be 7 or 9.
If d would be 7, e would need to be 3 or 4, which is impossible, since f or h are 3 and 4.
d = 9.
e+ (3,4) = 9 => e:={6, 5}, but since g is 6 or c is 6, e=5 and therefore f=4.

For a and b we have 1 and 7 left, which leads concluent to c=8.
But whether a or b are 1 or 7 is not decideable.

To verify my assumption I elegantly skipped the possibility to create a permutation, and let Random poof my assumption:

 We must storm this mad man's lab and destroy his villanous bomb! Are you with me tiny ad? a bit of art, as a gift, the permaculture playing cards https://gardener-gift.com