I found this problem in an old math exam and I am not able to solve it:
A credit card number has 14 digits and the sum of any three consecutive digits is 20. What is the value of x?
_ _ _ 9 _ _ _ x _ _ _ 7 _ _
Can anyone solve it with and explanation?
>>134654
I don't see any fancy solution.
There are 12 variables and 12 equations. This can be solved.
>>134654
easy
9 4 7 9 4 7 9 x 7 9 4 7 9 4
x has to be 4
>>134658
you're missing the point. if the fourth digit is 9, then the second and third must add up to 11, so that second+third+fourth=20.
but if the second and third add up to 11, then the first must be 9 again. so the first, fourth, seventh, tenth and thirteenth digit must be 9. the rest is just filling in numbers.
Thank you. Now I feel stupid.
>>134699
Honestly, it also leads to the same thing.
a+b+c=20
b+c+9=20
a=9
c+9+d=20
b=d
and so on
>>134654
Or just note that
a+b+c=b+c+d=20, so a=d
thus every 4th digit repeats.
So fill out the 4th digits and the cc number is
9x79x79x79x79x
So 9+x+7=20; x=4
