Ask yourself “what if” questions: You need to be sure to go back to the original problem at the end, but wishful thinking can be a powerful strategy for getting started.
You have to go back and see if the clock can actually break apart so that each piece gives you one of those consecutive numbers.
Maybe you can solve the math problem, but it does not translate into solving the clock problem.
The goal is to find the underlying math problem, then come back to the original question and see if you can solve it using the math.
Of course, solving the question about consecutive numbers is not the same as solving the original problem.
It would be much more appealing to find a pattern in the smaller boards and then extend that pattern to solve the problem for a 100 × 100 chess board just with a calculation.
If you have not done so already, extend the table above all the way to an 8 × 8 chess board, filling in all the rows and columns.
If you add the numbers in each piece, the sums are consecutive numbers.
(Consecutive numbers are whole numbers that appear one after the other, such as 1, 2, 3, 4 or 13, 14, 15.) Can you break another clock into a different number of pieces so that the sums are consecutive numbers?
This is all well and good, but how do you actually do these steps?!?! We will articulate some useful problem solving strategies, but no such list will ever be complete.
This is really just a start to help you on your way.