If you like the Genius Square, the same Happy Puzzle Co 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.

Part of what makes it work is the head-to-head option. Two players each take a grid, roll the same starting positions, then race to finish first. A single round takes only a few minutes, which makes it easy to fit in before dinner or on a rainy afternoon. It suits ages six and up, and adults tend to get just as competitive as the children.

Stocking fillers are where the smaller puzzles shine. Self-contained games such as the Genius Square, along with pocket brain teasers, drop neatly into a stocking and give someone a challenge for the quiet bit of the morning. For children, a game matched to their age, from Bee Genius for the little ones to WordSnap XL for older siblings, tends to get more play than yet another plastic toy.

Snakes and Ladders is one of the first board games most children learn, and for good reason. The rules could not be simpler: roll the dice, move your counter, climb a ladder if you land at the foot of one and slide back down if you meet a snake. There is no reading and no strategy to master, so even three and four-year-olds can join in and stand a fair chance of winning.

The 3D and giant multi-storey versions bring something new to the classic. Instead of a flat board, counters travel up and around a tall structure, with the snakes and ladders running between levels, which children find far more exciting to watch. Larger garden versions scale the whole thing up for outdoor play, so the game moves from the kitchen table to the lawn on a sunny day.

For a shortlist of compact games that pack down small and set up fast, browse the travel-friendly games chosen by games for children.