If you like the Genius Square, the same puzzle idea runs through a small family of games. Genius Star adds a bonus mechanic and a different set of pieces, Genius Gems and Genius Connection change the shapes and the goal, and Bee Genius is pitched at younger children who are new to shape puzzles. Each one keeps the roll-and-fill pattern while giving you a fresh challenge.

For a bigger group, party and bluffing games give teenagers and adults something to sink their teeth into. Titles such as The Traitors board game and card game, both available from The Happy Puzzle Company, lean on reading the room and second-guessing each other, which tends to spark the loudest laughs of the night. Keep one of these for when the whole family is together at Christmas or on a birthday.

If you want a shortlist of games tested for family play and grouped by how long they take, browse the family and party games chosen by brain games for adults.

Brain teaser puzzles for adults come in a few broad styles. There are mechanical puzzles, such as interlocking metal or wooden pieces you have to take apart and put back together, logic puzzles that ask you to work out a single correct arrangement, and spatial puzzles where you fit shapes into a fixed space. Knowing which type someone enjoys makes it much easier to choose one they will actually sit down with.

To see jigsaws grouped by piece count and theme, from first puzzles for toddlers to harder pieces for adults, take a look at the jigsaw collection at puzzles and games.

For gift ideas sorted by age band, with the number of players and rough playing time listed for each, browse the games-by-age pages at family board games.