I first came across and enjoyed a Futoshiki puzzle in the Guardian puzzles section.

Work out the digit that goes in each cell. In this 4×4 example, the digits from 1 to 4 must appear exactly once in each row and column.

Initially, some digits might be revealed and additionally, the board might also contain some inequalities between the board cells; these inequalities must be respected and following them will help you find the missing digits.

In the above puzzle, difficulty level, easy, we see that the fourth column already has a 1 and a 3, the remaining digits 2 and 4 can only be placed one way as we have to follow the inequality sign.

On Futoshiki.org from Vlad Daskalu, you can generate puzzles of sizes from 4×4 to 9×9 and choose one of 4 difficulty levels.

Other sites offering these puzzles include Brain Bashers where you can play a wide variety of puzzles, see the choice from the home page. 

There is, of course, an app for that, you’ll find Futoshiki available for Android and iOS.  The holidays offer a chance to explore some more puzzle apps and games. I have some details of various apps on this page.  Have you tried PhotoMath? Some of my Sixth Form students were checking some integration examples using this recently, it seems very easy to use and for the examples I tried looked very helpful.

MEI’s Sumaze series is most impressive, I think I’ll try Sumaze Adventure this Christmas.

For many more online puzzles to amuse you over the holidays try the Puzzle collections on Mathematics-Games.

Yohaku is a puzzle that will test your number sense and problem-solving skills. Each Yohaku puzzle is either an additive or a multiplicative puzzle. You must fill in the empty cells such that they give the sum or product shown in each row and column as well as satisfying a rule if given.