Cross-figure puzzles

Sample cross-figure puzzle Cross-figure puzzles are extremely challenging numeric crossword puzzles, in which the clues provide mathematical hints about the numbers in the grid. To my knowledge, the first Cross-figure puzzle was published by Henry E. Dudeney in 1926. These puzzles can take several hours to solve and finishing the puzzle is very satisfying indeed!

Back in 2010, I was contacted by Yochanan Dvir, who provided me with a scan of one of his collections of original Cross-figure puzzles - a kind of numeric crossword puzzle. Those puzzles are published here. In order to publish them, I transcribed his clues, and then wrote a script to parse the clues and solve the puzzles, thus insuring that the puzzles were transcribed correctly. Here are my transcriptions of those puzzles, published with Dvir's permission.

Dvir told me that he learned the art of making these puzzles around 2000 from the then 90-year old L. G. Horsefield. Horsefield published three sets of these puzzles in the early 1970s with Tandem publishing, probably around the time he retired. These books are now long out-of-print. I have managed to buy a few on EBay. Here are Dvir's puzzles, which very much resemble the puzzles of L. G. Horsefield.

Puzzles 1-20
Puzzles 21-40
Puzzles 41-60
Puzzles 61-80

Here's a little info about the puzzle constructor:

Yochanan Dvir

Born in the year 1923 in Warsaw (Poland), survivor of the Holocaust and Warsaw Ghetto, Yochanan Dvir has lived since 1946 in a small community in Israel.

A mechanical engineer by education, he published several technical books and lexicons.

"At the end of the last century, I received two books of Cross-figures. I liked them and began to construct such puzzles on my XT computer, mostly for myself to solve. When I had eighty puzzles saved, I printed them in pocket-book format and even sold three copies on Amazon.com.
Some years later I found that I enjoy children's literature, stories, folk and fairy tales (maybe a sign of senility?). My granddaughters were just in the book-reading stage, so I began to translate stories into Hebrew for them, from about seven or so foreign languages which I could read and understand.
In the year 2005, I began to publish the stories on my website www.sefer-li.net, (which means "my book") and today there are over 1,500 such stories, mostly illustrated, on my site, with several hundred visitors daily. All this I've built and managed myself from scratch."

Cross-figures by Krazydad

In 2026, I finally got around to making some Cross-figures of my own! Here are two books of them, in two different styles. Classic, which are modeled after the puzzles of L.G. Horsefield and Y. Dvir, and Modern, which are influenced by the innovations of Rainer Typke (see below).

Classic Cross-figures (100 puzzles)
Modern Cross-figures (100 puzzles)

I also prepared this handy Cheat Sheet listing primes, squares, cubes, triangular, Fibonacci, and perfect numbers to help with solving.

Looking for more cross-figure puzzles? I highly recommend the book Crossnumber Puzzles by Rainer Typke, which you can buy on Amazon. This book contains 50 handmade puzzles of varying difficulty (most are quite difficult, in my opinion). Enjoy!

Neil Aggarwal's has provided some TripleCross puzzles, a hexagonal Cross-figure variant that has three axes. His website, 3DMathPuzzles.com contains other cross-figure-inspired puzzles. Neil's puzzles are very clever and fun (and extremely challenging) to solve. I highly recommend them!

Professor Emeritus William Sit has written a fascinating paper on cross-figure puzzles (On Crossnumber Puzzles and the Lucas-Bonaccio Farm). This paper includes a very challenging and interesting puzzle.