 # Did you solve it? Argentina’s creative genius

Earlier today I set you these three challenges by Argentina’s puzzle guru Rodolfo Kurchan. Here they are again with solutions.

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.

Solution

92335 + 92335 = 184670

(The other solution it is 52339 + 52339 = 104678)

Here’s one way you might have gone about it. You are looking for the largest Messi, so let M = 9. Straight away F = 1, and U = 8. E + E must be less than 10 (since there is no carry), so E is 0, 2, 3, or 4. We can eliminate E = 0, since this would mean that T is either 0 or 1, which would be impossible. We can also eliminate E = 4, since this would mean T is 8 or 9, which is also impossible. Thus E = 3 or 2.

The number zero cannot be S, since this would mean either O or B is also zero. Nor can it be I, since this would make L zero. Nor can it be T since, this would give a carry to the M column. We can also see how zero is not B or O, since this would mean that S is 5, which cant be because if S is 5 then B would be 1, which is already taken. So L = zero. Which means I = 5

We know E = 3 or 2. Let’s say E = 3. Then T = 6 or 7. If it T = 6, then there is no way of rearranging 2, 4 and 7 among the other letters to make the equation work. And it doesn’t work with T = 7 either. So E is not 3.

Let E = 2. T must be 4, and then with a Messi-like flourish, you finish with S = 3 and O = 7 and B = 6

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.

Solution

ii) and iii) The left fits on a 12 x 12 grid, since you need to divide one side by 4 and the other by 3. The right on a 10 x 10 grid, since you need to divide one side by 5 and the other by 2. (Apols for rubbish sketches.)

iv) and v)

2. 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. The path stops because there is nowhere to put the 3 without breaking the rule of not repeating numbers in the same row or column.

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?

Solution:

I hope you enjoyed today’s puzzles. I’ll be back in two weeks.

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.

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.