The convolution series question is bad 'cos you don't give enough terms to even see it. The next term is 28 only if the first four numbers are 1,5,7,15 and you assume that what precedes 1 is 0. If you give two or three terms more (28, 48, 75), I'm sure more people will have success figuring it out. The number of terms given is like saying "1 1 2 ?" and saying the missing one is 3 because this is the Fibonacci series.
In any case, even if the candidate didn't figure out the convolution series, but vocally tried calculating differences or tried to look at the numbers in a different base than 10 or even complained that she can cook up an arbitrary rule for the remainder of the series, that kind of thought process is certainly interesting and playful interview material .... if the post calls to a keen eye for patterns. The key is that the answer is not what you're interested in, ever. It's always the thought process.
In any case, even if the candidate didn't figure out the convolution series, but vocally tried calculating differences or tried to look at the numbers in a different base than 10 or even complained that she can cook up an arbitrary rule for the remainder of the series, that kind of thought process is certainly interesting and playful interview material .... if the post calls to a keen eye for patterns. The key is that the answer is not what you're interested in, ever. It's always the thought process.