MEM/STACK

How it works

Named slots hold numbers. You see them once. Instructions then rewrite them one at a time, and you keep up in your head. At the end you answer questions with nothing on screen.

The loop

1. See the slots, scattered. Names above values.
2. Track each instruction as it flashes. Nothing is shown twice.
3. Answer one to three questions on a blank screen.
4. Review the replay, which shows where you diverged.

The slots land somewhere new every round, never in a row. A row can be held as a list and the names read back off the order at the end. Scattered, B has to be remembered as B.

A wrong answer or a timeout costs one strike, however many questions you missed that round. Three strikes end the run. Failing does not send you backwards: the level runs again with new instructions.

A level takes three clears to pass. The marks beside the level number show how many you have banked. A strike does not spend them.

Level 1 is one instruction over two slots, A and B, and so is level 2. Level 3 adds a third slot and nothing else. Level 4 adds the second instruction, level 6 the third. Nothing ever gains a slot and an instruction on the same level. New vocabulary arrives one idea at a time, and a new idea appears at most once per round while it is still new.

Rules worth knowing

Reads happen before writes

An instruction reads the state as it was when it began, then applies every change at once. "Everyone becomes the total" uses the total from before anyone changed.

Except after "then"

In a two-part instruction, the second part sees what the first did.

The difference cascade

Each slot becomes the distance between it and the slot to its right. The last slot is untouched. All computed from the state before the cascade ran, so 8 12 3 becomes 4 9 3.

The middle value

With an even number of slots there are two middles. Always the lower.

Rotating

"Rotate every value right" moves each value one position right, and the last wraps to the front. The slots do not move. The values do.

Ties never happen

You are never asked which slot is largest when two are tied, or to divide something that does not divide.

Scoring

Your score is the highest level you passed. Ties break on strikes remaining, then on speed. Answering inside par scores full speed. Past par it decays, and well past it the question closes.

The difficulty model

No level here was authored. Each one is generated, simulated, and kept only if its predicted difficulty lands within 10% of that level's target.

What difficulty is

You are modelled as a store plus a processor. The store holds items: slot values, half-finished arithmetic, the question you are holding. Mistakes happen only at accesses, the moments you reach into the store or compute something. Each access carries a failure probability that rises with three things:

• Load, how many items you hold at once.
• Age, how long since you last touched the one you need.
• Tempo, how little time you are given.

Every instruction and question compiles to a trace of primitive events. The trace is priced, and the round's total is one number: strain. Your predicted chance of getting the round right is e−strain.

A step is priced by what it asks for, not only by how big the numbers are. A multiplication costs more than an addition. Working out which slot is the largest costs more than reading one you already know.

Why not a difficulty setting

Because this is falsifiable. The model claims a scan late in a round costs more than the same scan early, and that rotating the slots makes every value read as stale. Those are predictions, and the game records enough to check them. If the numbers disagree with players, the numbers are wrong.

Settings

Nothing here changes reading time, processing time, gaps, or par. Difficulty is not configurable.

Saving progress

Practice

Unscored. Holds one level for as long as you want, and can slow the tempo.

Your data

Practice

Unscored. Strikes still end the session, but nothing is recorded.

Practice stays on the level you pick. Clearing a round draws another at the same level.