Four questions, one idea: the smallest that will do, and why nothing smaller will.
The answer key prints on a separate page.
Section 1 is a shop whose coins defeat the rule everyone uses — take the biggest that fits — and a child can prove it by counting both answers. Section 2 gives two unmarked jugs and asks for the fewest steps, which cannot be counted from the outside: it has to be searched, and then shown to be as short as possible. Section 3 has almost no arithmetic in it at all. It turns on noticing that a balance says one of three things, not two, so each weighing divides the suspects by three — and that a child who splits the pile in half is discarding a third of what the scale told them. Section 4 is a bug crossing the surface of a box: the shortest route is a straight line once the two faces it crosses are unfolded flat, and cutting through the box is shorter but not allowed.
That is the order, and it is the point. The sheet moves from a minimum you can check, to one you have to find, to one that depends on how much information an instrument gives you, to one that is a distance rather than a count. One question per section, because each answer is a route the child writes out rather than a number they produce.
