How to play Undo Machine
- Choose a formula and look at the forward machine: the unknown goes in on the left.
- Read it from the right: the last operation is the first one to undo.
- Build your machine from inverse boxes: − for +, ÷ for ×, √ for a square, and the other way round.
- Press Play and follow the value through your boxes. It should come out as the unknown.
Undo operations in reverse order
A formula tells you what happens to a quantity, step by step. In x = x₀ + v·t, the time is first multiplied by v and then x₀ is added. To find t from x, run those steps backwards: first subtract x₀, then divide by v. It is like taking off shoes and socks: what went on last comes off first. Each step is undone by its inverse: subtraction for addition, division for multiplication, and a square root for a square.
A focused learning model
A formula is shown as a chain of single operations on the unknown, using the values of one real situation. Your machine is a chain of up to six boxes, applied in order to the known value. The token spends 0.8 s on each stretch of pipe, so a run lasts 0.8 s for every box, plus 0.8 s. A result counts as right when it equals the true value to within rounding.