mathmates problem 33

Mathematics
Tutor: None Selected Time limit: 1 Day

Some digits are missing from this credit card number. If the sum of any three consecutive digits is 20, what is the value of x?

_ _ _5 -  _ _ _ _-  x_ _ _ - _8_ _

Jan 9th, 2015

If you consider the sequence as: a, b, c, 5, d, e, f, g, x, h, i, j, k, 8

You then set up equations like:

a+b+c = 20 ...(1)
b+c+5 = 20 .... (2)
c+5+d = 20
5+d+e=20
d+e+f=20
e+f+g=20
f+g+x=20
g+x+h=20
x+h+i=20
h+i+j=20
i+j+k=20
j+k+8=20

You then find solutions like:
from eq(2)

b+c+5 = 20
or, b+c = 20-5 =15

put this in eq (1),
a+15 =20
you get,
a=5


similarly, you can find,
b=d
c=e
f=5
g=b
x=c
h=5
i=b
j=c

k=5
b=8


If a = 5 and b = 8, then c = 7. Since x = c, x = 7.


Please best my answer and add me as your tutor for further help. Thanks :)

Jan 9th, 2015

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