# Solving math word problems WITHOUT brute force

How can we solve these problems withing using brute force?

http://edhelper.com/math/multiplication51.htm

• What is brute force? Is it using logic to reduce the number of possible cases, then testing those? – The Chaz 2.0 Nov 3 '11 at 14:53
• It also looks like they are intended for 5th graders. I'm working on applying some logic to it now. Brute force would be writing a computer program in order to solve this or (shudder) manually trying every combination. I think we can do better.. – foodals Nov 3 '11 at 14:53
• this can be done by applying systems of equations with several variables – Peđa Terzić Nov 3 '11 at 15:06
• pedja, how? can you show an example? – foodals Nov 3 '11 at 15:11
• These are known as "cryptarithms" or "verbal arithmetic". You can get started in Wikipedia's page on solving them. As the page notes, one usually uses a mix of logic to eliminate possibilities and reduce to a small number, and then a bit of trial-and-error. – Arturo Magidin Nov 3 '11 at 16:31

AND$\times$NOT$=$SOCKS
$(100A+10N+D)\times(100N+10O+T)=10000S+1000O+100C+10K+S$
So you have to calculate left hand side.You will get expression similar to the right hand side. Use fact that equality is true if corresponding coefficients are equal.Applying this condition you should get $5$ equations with $8$ unknown variables.
• $A\cdot N=S$ or $D \cdot T=S$ for example... – Peđa Terzić Nov 3 '11 at 16:07