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.

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

a = 7
b = 4
c = 6
d = 5
e = 8

substituition for b

^ 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...

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!

C4 and a detonator!

But C=6, not 4...?



Sorry....
Ed.

I did it by substituting for b and I also did it by matrices

quote:

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Originally posted by liam.mccaffrey
I did it by substituting for b and I also did it by matrices

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quote:

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Originally posted by Madinventions
But C=6, not 4...?



Sorry....
Ed.

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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