Did you solve it? Argentina's creative genius

Earlier today, I brought you these three challenges from Argentinian puzzle guru Rodolfo Kurchan. Here they are again with solutions.

1. Messi math

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

Solution

92335 + 92335 = 184670

(The other solution is 52339 + 52339 = 104678)

Here's one way to do it. You're looking for the greatest Messi, so let M=9. Right away F=1, and U=8. E+E must be less than 10 (since there's no carry), so E is 0 , 2, 3, or 4. We can eliminate E = 0, because that would mean that T is either 0 or 1, which would be impossible. We can also eliminate E = 4, because that would mean that T is 8 or 9, which is also impossible. So E = 3 or 2.

The number zero cannot be S, because that would mean that O or B is also zero. Nor can it be I, since that would make L zero. It also can't be T since that would give a carry to column M. We can also see how zero isn't B or O, since that would mean S is 5, which can't 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's T=6, then it there's no way to rearrange 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, then with a flourish a la Messi, you end with S=3 and O=7 and B=6

2. A game of four parts

For each of the five tasks below, you have to 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 than the first two).

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

v) No two pieces are the same size .

Here is a solution for the first one. The square is divided into four triangles of the same shape and size.