liam.mccaffrey
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| posted on 28/8/09 at 12:26 PM |
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Friday Numbers Quiz
You need to generate a 5 digit code to open a door.
The fifth number plus the third number equals fourteen.
The fourth number is one more than the second number.
The first number is one less than twice the second number.
The second number plus the third number equals ten.
The sum of all five numbers is 30.
There are a bunch of ways to do work this out. Please state your method.
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alistairolsen
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| posted on 28/8/09 at 12:35 PM |
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so the rules are:
a+b+d=16
d=b+1
a=2b-1
b+c=10
c+e=14
substituting the second and third into the first formula gives us
16=2b-1+b+b+1 or 16=4b or b=4
from the second formula we can find d=5
from the third we can find a=7
c is therefore 10-b which is 6
and e is 14 - 6 which is 8
Quick check tells us 4+5+6+7+8 = 30
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02GF74
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| posted on 28/8/09 at 12:38 PM |
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a = 7
b = 4
c = 6
d = 5
e = 8
substituition for b
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Mr Whippy
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| posted on 28/8/09 at 12:46 PM |
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^ all very cleaver I’m sure, except simply typing -
"The fifth number plus the third number equals fourteen"
into google gives thousands of solution examples...
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Madinventions
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| posted on 28/8/09 at 12:47 PM |
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eq1: e+c=14
eq2: d=b+1
eq3: a=(b*2)-1
eq4: b+c=10
eq5: a+b+c+d+e=30
Therefore: a+b+d = 16 (given eq1 and eq5)
d=b+1, so a+b+b+1 = 16
a=(b*2)-1 so b+b-1+b+b+1 = 16
Therefore 4*b = 16, so b=4.
b+c=10 (eq4) so c=6
e+c=14 (eq1) so e=8
d=b+1 (eq2) so d=5
a=(b*2)-1 (eq3) so a=7
a=7
b=4
c=6
d=5
e=8
a+b+c+d+e=30
Ed.
Thanks for that - it woke my brain up momentarily!
Mojo build diary: http://www.madinventions.co.uk
Solo music project: Syrrenfor http://www.reverbnation.com/syrrenfor
View my band website:
http://www.shadowlight.org.uk
http://www.eastangliankitcars.co.uk/
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Richard Quinn
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| posted on 28/8/09 at 12:48 PM |
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C4 and a detonator!
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Madinventions
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| posted on 28/8/09 at 12:50 PM |
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But C=6, not 4...?
Sorry....
Ed.
Mojo build diary: http://www.madinventions.co.uk
Solo music project: Syrrenfor http://www.reverbnation.com/syrrenfor
View my band website:
http://www.shadowlight.org.uk
http://www.eastangliankitcars.co.uk/
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liam.mccaffrey
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| posted on 28/8/09 at 12:50 PM |
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I did it by substituting for b and I also did it by matrices
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02GF74
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| posted on 28/8/09 at 01:03 PM |
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quote:
Originally posted by liam.mccaffrey
I did it by substituting for b and I also did it by matrices
that is correct - look for the number (b in this case) that appears most often in the other equations and substitute it in. simples.
dunno about your mattress method, think I'll sleep on it,
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Mr Whippy
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| posted on 28/8/09 at 01:08 PM |
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Richard Quinn
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| posted on 28/8/09 at 01:08 PM |
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quote:
Originally posted by Madinventions
But C=6, not 4...?
Sorry....
Ed.
Can use C6 if you prefer. Different composition but same overall effect!! 
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Staple balls
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| posted on 28/8/09 at 01:15 PM |
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Why are we generating this code?
If we need to break in, I'll just check which buttons are shiny.
If we're making a security code based on a maths teaser, we might as well not bother and just leave the door unlocked
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