Can you solve it? Argentina’s creative genius

To celebrate Argentina’s World Cup victory eight days ago, today’s puzzles are set by Rodolfo Kurchan, an internationally renowned puzzle inventor and author from Buenos Aires.

1. Messi maths

Replace the ten letters of the following sum with the ten digits 0,1,2, … 9, such that the sum is correct. Each letter represents a unique digit. There are two solutions, so find the one with the largest MESSI.

2. A game of four parts

For each of the five tasks below, you must divide a square into four parts that have the same shape, but whose sizes are determined by the following statements:

i) All four shapes are the same size.

ii) Only three are the same size.

iii) Two are the same size, and the other two are also the same size (but a different size from the first two).

iv) Two are the same size, and the other two are different sizes.

v) No two parts are the same size.

Here’s a solution for the first one. The square is divided into four triangles that are the same shape, and the same size.

For clarification: within each solution, the four parts must have the same shape. It is only their sizes that may change. However, each solution may involve a different shape. One solution fits perfectly along the lines of a 12 x 12 square, one on a 10×10 square, and one involves triangles.

Note: the fifth one is extremely difficult. Come back for the answer later.

3. Snake paths

Your goal in this puzzle is to create a path of digits in a 5×5 grid that goes 1,2,3,4,5 and then repeats the digits in a loop. The path can start in any cell, and moves horizontally or vertically, but never diagonally, and cannot cross itself. Digits cannot repeat in the same row or column (just like Sudoku). Here’s an example of a path of length 12.

Can you find a path that has length 19, the maximum possible?

Extra challenge: What is the longest path you can make in a 7×7 grid starting with 1 and then repeating the numbers once you get to 7?

I’ll be back at 5pm UK with the solutions.

PLEASE NO SPOILERS (although giving tips and hints is fine).

Thanks to Rodolfo for supplying today’s puzzles. To find out more about him here’s his website, and if you are strolling down Buenos Aires you can visit his philately shop.

Finally, festive best wishes to everyone who reads these puzzles. This year, the column received 4 million page views, almost double the amount it received in 2021. In keeping with the journalistic tradition of ‘best of the year’ lists, the three most popular posts were this one about Elon Musk, this one about engineering, and this Oxford university admissions question. Thanks to everyone who has enjoyed the puzzles, corrected my mistakes and sent in suggestions. Keep them coming, and see you in 2023!

I set a puzzle here every two weeks on a Monday. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.

I give school talks about maths and puzzles (online and in person). If your school is interested please get in touch.