This riddle had its tug-of-war, but in the end we got to the sweet middle. Surely new mathematical and general knowledge has been acquired. Thanks to Regla, to PROA, to RARJ for their outstanding participation.

Let's take it one step at a time.

### I

Every December 4th, in various parts of the world, tribute is paid to one of the most appreciated religious idols. For some, it is Saint Barbara, distinguished among the fourteen Holy Help of Christians of the Catholic Church; for others it's Changó.

On December 7, Antonio Maceo Grajales and his assistant Panchito Gómez Toro fell in combat. The Bronze Titan continues to win battles.

a With the 6 digits 4; 1; 2 ; 7; 1; 2; Construct the number of your sum. Using each digit only once. The Four Arithmetic Operations, No Parentheses

Just add those digits together and the answer is ready.

This question had an obvious answer. On many occasions, the obvious in a mathematical puzzle generates suspicion in those who have a good command of mathematics.

I thought about saying the number of its sum backwards, but I wanted to do the experiment.

Congratulations to PROA=...

b With the three digits of 412; build number 712; and vice versa. Anything goes, any operator and up to three times each digit, and as many parentheses as you want. Of course, the most efficient ones will be congratulated.

42*12+42*(4+1)-4/2= 504+210-2= 714-2=712

71*(7-1)-7*2= 426-14=412

Congratulations to RARJ

(4+2)!-4x2x1=712((7-2)!-17)x2x2=412

And at the bow

(1+1+4)!-4*2=6!-8=720-8=712(7+1)^2*7-(7+1+1)*2^2=8^2*7-9*4=64*7-36=448-36=412
.

As you can see, RARJ achieved greater efficiency by using fewer elements (digits and operators)

c Which of the following 10 words relate to Santa Barbara

Nicomedia

Snake

Celina

Dentist

Julienne

Lightning

Catholicism

Dioscorus

Baseball

Sword

Nicomedia (birthplace), Celina (with her son Reutilio turned Que viva Changó into a hymn), Juliana (her friend who was martyred with her), Rayo (people pray to Santa Barbara to be free from the lightning of the storms), Catholicism (she is part of the Catholic Church), Dióscoro (her father) and Espada (a symbol of unwavering faith)

Congratulations to Regla.

As an extra value, I leave you with the lyrics of the song Santa Bárbara by Celina Y Reutilio

Blessed Saint Barbara, for you my lyre arises

And with emotion he is inspired, by your beautiful image

Long live changó Long live changó

Long live changó Gentlemen

With infinite will, I tear from the heart

the melodious expression, asking that from heaven

Send us your consolation and your holy blessing

Long live changó Long live changó

Long live changó Gentlemen

Venerated and pure Virgin, Blessed Saint Barbara

Our favorite prayer, we carry you up to your height

Long live changó Long live changó

Long live changó Gentlemen

With joy and tenderness, I want to take my trovada

Out there in your sacred mansion, where good shines

By your divine cup, and your most holy sword

Long live changó Long live changó

Long live changó Gentlemen

On behalf of my nation, Santa Barbara, I ask you (bis)

May you water with your fluid, your sacred blessing

Long live changó Long live changó

Long live changó Gentlemen

I, too, from my heart, will give you my murmur

With pride and might, I'll make your name go up

And in the name of my Cuba, I send you this greeting

Long live changó Long live changó

Long live changó Gentlemen

d Which of the following 10 words are related to Antonio Maceo

Jetty

The Abra

Punta Brava

Jamaica

Chile

Peanut

Russia

Baraguá

San Luis

Hey

Malecón (his equestrian statue in that place); Punta Brava (Place where it fell); Jamaica (country of residence); Cacahual (the place where his mortal remains are kept); Baraguá (site of his historic Protest); St. Louis (birthplace); Che (born on the same day, and united in the history of Cuba)

Congratulations to Regla who incorporated two relevant pieces of information:

Jamaica, the place where his mother Mariana Grajales died

Frank País was born on December 7.

e I found at least three numerological curiosities between Santa Barbara and Antonio Maceo. It's kind of surprising.

Respuesta:

Ambas palabras tienen 12 letras.

Ambas tienen como dígito numerológico el 3. 102 y 129 es la suma respectiva.

1+0+2=3; 1+2+9= 12; 1+2= 3.

Pero además de estas dos el amigo RARJ encontró una tercera:

DN(Titán)=3
DN(Shangó)=3

También suele escribirse Shangó en lugar de Changó.

Felicitaciones a RARJ

### II

Acertijo "Lápices" a lo RARJ
Se tiene una balanza de platos.

De un lado hay 3 lápices redondos de diámetro 5mm y largo 15cm (1blanco, 1rojo, 1 negro).

Del otro lado hay 5 lápices hexagonales (3 verdes, 2 azules)

Antes de dar las respuestas es correcto decir que tuvimos dificultades en la redacción e interpretación de parte del acertijo.

Sabemos que en ocasiones una redacción confusa ha motivado el análisis creativo de los acertijandos, de manera que le dan sentido a dicha redacción.

I sent a first clarification, which after exchanging with RARJ, I decided to rectify and propose a second one that I now reiterate:

Néstor del Prado Arza says:

Attention ATTENTION.
Another version of subparagraph II.
The regular hexagon is inscribed on the circumference of diameter equal to 5 mm. From there you can calculate the side of the hexagon and apothegm.

So let's go with the answers

a If the scales are balanced, and the materials of construction are identical, how long are the hex pencils if all 5 are the same length?

We can infer that the side of the regular hexagon is 2.5

And calculate the apothegm of the hexagon, using the Pythagorean theorem.

Its value is 2.17.

The area of the regular hexagon is given by 6*2.5*2.17/2= 16.24 mm^2

The data in the figure does not correspond to that of the riddle, but it can help those who are less advanced in geometry.

The volume of the plate that we will consider on the left is given by

3.14*2.5^2*150*3= 8831.25 mm^3

On the right plate it would be: 16.24*L*5; where L is the length of the hexagonal pencils. By equalizing the volume on both plates, it is easy to clear the value of the length of the hex pencils (108.77 mm).

The Venezuelan friend PROA deserves to be congratulated for his reasoning, even if there is a miscalculation in his answer

b If 1 round pencil is passed to the hexagonal pencils, and 2 hex pencils are passed to the round pencils and the balance is balanced, how long are the hex pencils if the round pencils maintain their size? It's obvious that these are new pencils.

We have assumed that the left plate will be left with two round pencils and two hexagonal pencils with a new length. And on the right plate we will have a round pencil transferred to the left plate, and three hexagonal pencils with a new length (RARJ told me that they took out nibs)

Then, when the scales are balanced, we will have an equation in which we will have to clear the length of the new hexagonal pencils.

Left Plate (4 pencils; 2 round and two hexagonal)

Volume = 2943.75 +2943.75+ 16.24*L*2

Right plate (4 pencils; 1 round and three hexagonal)

Volume= 2943.75+ 16.24*L*3

2943.75 +2943.75+ 16.24*L*2= 2943.75+ 16.24*L*3

L= 181.27 mm

It is possible to make other interpretations, but I leave that to you.

I would like to congratulate PROA again for its reasoning.

Of course, he has every right to prove that both in the previous paragraph and in this one his answer is the correct one.

c After the movement made in the b, how are the colors distributed? Put a good cacumen on it.

We have two variants

Plate A Black-Red-Green-Green, adds up to 19. White-Blue-Blue-Green Plate B, adds up to 19

Plate A White-Red-Blue-Green, adds up to 19. Plate B Black-Blue-Green-Green, adds up to 19

First to reveal the crux of the solution, which is the number of letters of each of the five colors, that was the call to put a good cacumen on it.

We will use the table of the 8 combinations made by Regla

1) A: N-R-Az-Az and B: Bl-V-V-V; 17-21
2) A: N-R-Az-V and B: Bl-Az-V-V; 18-20
3) A: N-R-V-V and B: Bl-Az-Az-V; 19-19
4) A: BL-N-AZ-AZ and B: R-V-V-V; 19-21
5) A: Bl-N-Az-V and B: R-Az-V-V; 20-18
6) A: Bl-N-V-V and B: R-Az-Az-V; 21-17
7) A: BL-R-AZ-AZ and B: N-V-V-V; 18-20
8) A: Bl-R-Az-V and B: N-Az-V-V; 19-19
9) A: Bl-R-V-V and B: N-Az-Az-V; 20-18

So we have two possible answers:

3) A: N-R-V-V and B: Bl-Az-Az-V; 19-19
8) A: Bl-R-Az-V and B: N-Az-V-V; 19-19

Once again we must recognize the creativity of our friend PROA=...

Don't miss this lateral thinking response.

In the world of reds and blacks, inclusion and non-discrimination are the main things, so one blue and one green arrives. Then the white leaves to leave with one blue and two greens.