What this site is
Every puzzle here is written out in full: the statement, the constraints that bound it, two hints that can be opened one at a time, the answer, and a derivation with margin notes explaining why each step is allowed. The answer alone is never the point.
The figures that head each puzzle are generated from the puzzle itself — the tags and the difficulty tier decide the shape of the tessellation — so no two entries look alike, and no stock imagery appears anywhere on the site.
How the three tiers work
Warm-up problems turn on a single idea and are meant to be finished in a minute or two. Core problems chain two or three moves and are the ones worth writing down. Olympiad problems are competition-shaped: the first move is rarely the obvious one, and the proof carries the weight.
- Warm-up — one observation, one line of reasoning.
- Core — two or three ideas, occasional algebra, a proof sketch that needs care.
- Olympiad — parity, invariants, extremal arguments and the standard competition toolbox.
When new problems appear
Problems are added on Mondays, Wednesdays and Fridays, one at a time. Nothing is published in bulk, and a page that has not been released yet simply does not exist: it is not teased in advance and it leaves no empty row in the listings.
The glossary
The glossary collects the vocabulary the solutions lean on — pigeonhole, invariant, monovariant, bijection, Vieta jumping and the rest — with a short definition, a worked example of the idea in use, and the mistake each term most often invites.
Corrections
Mathematics is a public activity and mistakes are part of it. If a derivation is wrong, incomplete, or quietly assumes something it should have proved, write to [email protected] with the puzzle title and the step at issue. Corrections are made in place and the date at the foot of the page is updated.
Who writes this
Slate & Sum is written and maintained by one editor working through the recreational and olympiad canon: parity arguments, the pigeonhole principle, generating functions, graph colouring, additive number theory and the classic competition problems that keep turning up in new clothes.