With notable absences, but with answers that will make us enjoy and think, this riddle happened. On behalf of all the riddles I send a message to Marlon, the youngest of our participants, wishing him a speedy recovery of his health.

Let's go in parts.

I

Determine the missing number and a training pattern

to 5; 7; 9; 11; 13; ¿?

Answer: 15

Pattern: 2n+3; n from 1 to 6

Recognition to those who succeeded, but did not work well the pattern.

b 5; 4; 3; 2; 1; ¿?

Find a pattern that uses a mathematical function

Answer: 0

Pattern with logarithm function; log(10^n); for n, from 5 to 0

log(10^5); log(10^4); log(10^3); log(10^2); log(10^1); log(1^0)

Recognition to those who succeeded, but did not work well the pattern.

C 3; 9; -3; 21; -27; 69; ¿?

Answer: 123

Pattern: (-2)^n+5; for n from 1 to 7.

It is a pity that Charlie did not participate, because in this paragraph I put 25 instead of 21, so that he could find out.

And another heavyweight in mathematics returns. SFFT, was dedicated to what RARJ called pea.

SFFT said:

For exercise 1 c... This could be one of the many solutions:

Xn=(263/60)*n^5-(205/4)*n^4+(2491/12)*n^3-(1355/4)*n^2+(5521/30)*n+ 3

For n belonging to the non-negative integers, greater than 0. For the exercise the term of the sequence that would follow according to this Lagrange interpolating polynomial would be: 1415. This answer is not unique.

Another possible answer for 1...c would be to define the following function in sections:

X0 = 3, for n=0

X1=9, for n=1

Xn= 38n^3+382n^2+1216n -1211, for n greater than 2, with n belonging to the naturals.

If we use this function to define the nth term of the sequence, 69 would be followed by 541.

II

Determine the missing word, applying creative logic and explain your answer

to Red; Black; White; ¿?

Answer: Magenta

Number of successive letters 4; 5; 6 and 7

Congratulations to RARJ

b Col; Watercress; Lettuce; ¿?

Answer: Carrot

Number of letters that grow in two. 3;5;7;9

Congratulations to RARJ

c Lis; Lily; Lily; ¿?

Answer: Margaret

Idem to the previous one in the growth of the name of the flowers.

d Two; Five; Fourteen; ¿?

Answer: Sixteen

Words with number of letters 3;5;7 and 9

Congratulations to RARJ

e One; Seven; Twenty-two; ¿?

Answer: Twenty-one

Number of vowels in the word that grows by 1; 2; 3; 4; 5

f Cat-Duck-¿?- Mole- Monkey- ¿?

Answer: Toad and Wolf

Vowel pattern a-o; and o-o.

Good answers from you, especially the following:

Paul 12 said:

Cat-Duck-Toad (the common factor is water since the cat fears it, the duck enjoys it and for the toad it is vital, especially in its initial stage of life)

.. Mole – monkey – wolf (common food chain factor, predatory wolf, mole and monkey prey).

III

The soup of meaningful words of the month of May.

I assure you that there are at least 14, if you reach ten I congratulate you.

Here are the ones I thought:

WORK; row eight on the left. Labor Day May 1

ONE; Row one, right, first day.

FEU; ascending diagonal; 52nd Anniversary First National Council of the FEU, May 22.

GAY;

COUNTRYSIDE; diagonally downward; Peasant habitat

NUÑEZ; sixth row on the left; Enrique Núñez Rodríguez, his centenary May 13

AFRICA; seventh column down; Africa Day

ANAP; seventh row on the left; National Association of Small Farmers

ANTON; first row on the left; writer Antón Arrufat.

IROEL; second row on the left, Iroel Sánchez dies

MOTHER; eighth column; his day on the second Sunday.

MARTI; ascending diagonal; Fallen in action on 19 May.

INRA; diagonal descending; National Institute of Agrarian Reform.

AN; seventh row on the right, twice National Assembly

BF; third row on the right; Musical group in dignified battle.

ORDA; diagonal descending; those of the fascists, defeated.

Some of you found other words, although they did not explain the justification for associating it with May. I consider almost all of them relevant.
BAR; GARLIC; BREAD; WATER; Peanut; ANNA; LOW; CZAR; PINEAPPLE; LOW; ARAN; JABA; WAVE; RICH; PAIR; LEO; LULLABY; RIA;

They will tell us what they thought to put them. The explanations may be different, although some brought by the hair.

I end with this tribute.

Yesterday, May 31, for many is considered the Day of the Mathematician, for the tragic death of the Frenchman Évariste Galois; the youngest and brightest human being, and not only in Mathematics.

With only sixteen years, interested in finding the necessary conditions to define whether an algebraic equation was capable of being solved by the method of radicals, he began to outline what would later be known as "Galois theory", analyzing all possible permutations of the roots of an equation that met certain conditions.

Through this process, which in current terminology is equivalent to finding the group of automorphisms of a field, he laid the foundations of modern group theory, one of the most important branches of algebra. Galois intuited that radical solubility was subject to the solubility of the related automorphism group.

Despite his revolutionary discoveries, or perhaps for that very reason, all the memoirs he published with his results were rejected by the Academy of Sciences, some of them by such eminent mathematicians as Augustin-Louis Cauchy, Joseph Fourier or Siméon Denis Poisson.

An active member of the anti-monarchist opposition, Évariste Galois was involved in a duel whose motivations still remain unclear today. Foreseeing his more than possible death in the lance, he worked feverishly on a kind of scientific testament that he addressed to his friend Auguste Chevalier. A few days later the duel took place and the mathematician, wounded in the belly, died a few hours later, without having reached the age of twenty-one.

See you on the first Monday of the sixth month of 2023.