Not Necessarily in That Order
Age 11 to 14
Correct solutions were received from:
Arun of the Vidya Niketan School, James from Poynton High School, Andrei from School 205 Bucharest, Grace and Kate from Bentley Park College, Sudeep from St Paul's Svhool and Dean from Hillingdon. Congratulations to you all.
Here is Sudeep's solution:
Smith is a programmer, Cooper is the mechanic, Jones is a teacher and Baker is a welder!
The teacher always walks to work. Both Baker and Cooper "take turns driving each other to work" so neither is the teacher.
Neither Cooper nor Baker can be a programmer because if either one is a programmer, the other one has to be a welder or a mechanic. This cannot work because while Baker and Cooper are neighbours, the programmer does not live near the welder and has only met the mechanic once.
This means that Baker and Cooper are the welder and mechanic, though not neccesarily in that order.
As Cooper earns more than Jones and Cooper is either a mechanic or a welder, Jones cannot be a programmer as the programmer earns more than the welder or the mechanic.
Therefore by elimination, Jones is the teacher and Smith the programmer.
The mechanic and the programmer have only met once, so Baker cannot be the mechanic as he regularly plays darts with Smith.
Therefore Cooper is the mechanic and Baker is the welder.