Randy, Sam, Tim and Will counted the number of puzzles they had solved in two months. Sam has solved twelve more than Tim. Randy had solved seventeen less than Sam.Will had solved twice as many as Randy. They have solved a total of 267 problems. How many puzzles did each person solve?

Tim -- x

Sam --- x+12
Randy -- (x+12) - 17 = x - 5
Will -- 2(x-5)

Tim+Sam+Randy + Will = 267

looks easy.

To solve this problem, we need to assign variables to the number of puzzles each person has solved. Let's say "x" represents the number of puzzles Tim has solved.

Based on the given information, we can deduce the following:

- Sam has solved twelve more puzzles than Tim, so Sam has solved x + 12 puzzles.
- Randy has solved seventeen less puzzles than Sam, so Randy has solved (x + 12) - 17 puzzles.
- Will has solved twice as many puzzles as Randy, so Will has solved 2 * [(x + 12) - 17] puzzles.

The total number of puzzles solved by all four people is 267:

x + (x + 12) + [(x + 12) - 17] + 2 * [(x + 12) - 17] = 267

Now, we can solve this equation to find the value of x.