Solution for Pay Rises ...

The one who opted for the half yearly pay rise got the job.

This is because the employers thought that person must be the more intelligent of the two applicants:

To see this, look at how the salary pans out for the two cases, noting that salary is paid half-yearly:

£3,000 yearly:

First year:  £10,000 + £10,000 = £20,000

Second year:  £11,500 + £11,500 = £23,000

Third year:  £13,000 + £13,000 = £26,000

Fourth year:  £14,500 + £14,500 = £29,000

£1,000 half yearly

First year:  £10,000 + £11,000 = £21,000

Second year:  £12,000 + £13,000 = £25,000

Third year:  £14,000 + £15,000 = £29,000

Fourth year:  £16,000 + £17,000 = £33,000

And so on and so forth.