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febrero 16, 2025

«PROMP» dado a DeepSeek:

Se quiere crear un grupo de 350 personas que quede proporcionalmente representado por este conjunto de 7 grupos

  1. La población de China
  2. La población de India
  3. La población de Rusia
  4. La población de Europa, quitando España y Portugal
  5. La población de España, Portugal, Méjico, América Central y América del Sur
  6. La población de Estados Unidos, Canadá y Groenlandia
  7. La población del Resto del Mundo

Calcúlame los representantes de cada grupo y razóname tu respuesta

Y DeepSeek contesta:

Para calcular el número de representantes de cada grupo de manera proporcional a sus poblaciones, seguimos estos pasos:

  1. Obtener las poblaciones estimadas (2023):
  • Grupo 1 (China): 1,425 millones
  • Grupo 2 (India): 1,412 millones
  • Grupo 3 (Rusia): 144 millones
  • Grupo 4 (Europa sin España/Portugal): 691 millones
  • Grupo 5 (España, Portugal, México, Centroamérica y Sudamérica): 670 millones
  • Grupo 6 (EE.UU., Canadá y Groenlandia): 377.056 millones
  • Grupo 7 (Resto del mundo): 3,280.944 millones
  • Población mundial total: 8,000 millones
  1. Calcular el porcentaje de cada grupo respecto al total mundial:
  • Grupo 1: ( \frac{1,425}{8,000} = 17.81% )
  • Grupo 2: ( \frac{1,412}{8,000} = 17.65% )
  • Grupo 3: ( \frac{144}{8,000} = 1.80% )
  • Grupo 4: ( \frac{691}{8,000} = 8.63% )
  • Grupo 5: ( \frac{670}{8,000} = 8.37% )
  • Grupo 6: ( \frac{377.056}{8,000} ≈ 4.71% )
  • Grupo 7: ( \frac{3,280.944}{8,000} ≈ 41.01% )
  1. Aplicar los porcentajes a 350 representantes y redondear:
  • Grupo 1: ( 350 \times 0.178125 ≈ 62.34 ) → 62 (redondeo inicial)
  • Grupo 2: ( 350 \times 0.1765 ≈ 61.78 ) → 61
  • Grupo 3: ( 350 \times 0.018 = 6.3 ) → 6
  • Grupo 4: ( 350 \times 0.086375 ≈ 30.23 ) → 30
  • Grupo 5: ( 350 \times 0.08375 ≈ 29.31 ) → 29
  • Grupo 6: ( 350 \times 0.047132 ≈ 16.50 ) → 16
  • Grupo 7: ( 350 \times 0.410118 ≈ 143.54 ) → 143 Total inicial: ( 62 + 61 + 6 + 30 + 29 + 16 + 143 = 347 ) (faltan 3 representantes).
  1. Distribuir los 3 escaños restantes usando los mayores decimales residuales:
  • Grupo 2 (0.775), Grupo 7 (0.541), Grupo 6 (0.496): se añade 1 a cada uno.

Resultado final:

  • Grupo 1 (China): 62
  • Grupo 2 (India): 62
  • Grupo 3 (Rusia): 6
  • Grupo 4 (Europa sin ES/PT): 30
  • Grupo 5 (ES/PT + Latinoamérica): 29
  • Grupo 6 (Norteamérica): 17
  • Grupo 7 (Resto del mundo): 144

Total: ( 62 + 62 + 6 + 30 + 29 + 17 + 144 = 350 ).

Razonamiento:
Se aplicó el método del resto mayor para garantizar la proporcionalidad y ajustar los decimales, asegurando que la suma total sea 350. Los grupos con mayor población (China, India y Resto del Mundo) obtienen más representantes, mientras que los menos poblados (Rusia) tienen menos.

Y el razonamiento de DeepSeek, en inglés, es el siguiente:

Okay, let’s tackle this problem step by step. The user wants to create a group of 350 people that proportionally represents seven different population groups. Each group corresponds to specific regions or countries as listed. The goal is to calculate how many representatives each group should have based on their population sizes.

First, I need to figure out the current population of each of these groups. The problem mentions seven groups:

1. China

2. India

3. Russia

4. Europe, excluding Spain and Portugal

5. Spain, Portugal, Mexico, Central America, and South America

6. United States, Canada, and Greenland

7. Rest of the World

Since the problem doesn’t provide specific population numbers, I have to look up the most recent data. Let me recall approximate population figures. As of 2023, China’s population is around 1.425 billion, India’s about 1.412 billion. Russia is around 144 million. For Europe excluding Spain and Portugal, I need to subtract Spain (about 47 million) and Portugal (10 million) from the total European population, which is roughly 748 million. So 748 – 47 -10 = 691 million.

Group 5 includes Spain, Portugal, Mexico, Central America, and South America. Spain and Portugal together are 57 million. Mexico is around 129 million, Central America approximately 50 million, and South America about 434 million. Adding those: 57 + 129 + 50 + 434 = 670 million.

Group 6 is the US (339 million), Canada (38 million), and Greenland (0.056 million). Total is 339 + 38 + 0.056 ≈ 377.056 million.

Group 7 is the rest of the world. To calculate this, I’ll subtract the sum of groups 1-6 from the total world population. The world population is roughly 8 billion. Let’s sum up the first six groups:

1. China: 1,425 million

2. India: 1,412 million

3. Russia: 144 million

4. Europe (excl. Spain/Portugal): 691 million

5. Group 5: 670 million

6. Group 6: 377.056 million

Adding these: 1,425 + 1,412 = 2,837; +144 = 2,981; +691 = 3,672; +670 = 4,342; +377.056 ≈ 4,719.056 million.

Subtracting from 8,000 million (world population): 8,000 – 4,719.056 ≈ 3,280.944 million for Group 7.

Now, I need to calculate the proportion each group represents relative to the total world population and then apply that proportion to the 350 representatives.

Let me create a table with each group’s population and then compute their percentage of the total, then multiply by 350 to get the number of representatives. Since we can’t have fractions of people, we’ll have to round appropriately, possibly using the largest remainder method to ensure the total is 350.

Wait, but let’s check if the user expects the sum of the groups to equal the world population. In my calculation, Group 7 is the rest, so the total should be 8,000 million. Let me verify the numbers again:

China: 1,425

India: 1,412

Russia: 144

Europe (excl. ES/PT): 691

Group5: 670 (ES+PT+MX+CA+SA)

Group6: 377.056 (US+CA+GL)

Group7: 3,280.944

Sum: 1,425 +1,412 = 2,837; +144=2,981; +691=3,672; +670=4,342; +377.056=4,719.056; +3,280.944=8,000. So that adds up correctly.

Now, calculate each group’s percentage:

Group1: 1,425 / 8,000 = 0.178125 → 17.8125%

Group2: 1,412 /8,000 = 0.1765 →17.65%

Group3:144/8,000=0.018 →1.8%

Group4:691/8,000=0.086375 →8.6375%

Group5:670/8,000=0.08375 →8.375%

Group6:377.056/8,000≈0.047132 →4.7132%

Group7:3,280.944/8,000≈0.410118 →41.0118%

Now multiply each by 350:

Group1: 350 * 0.178125 ≈62.34375 →62

Group2: 350 *0.1765≈61.775 →62

Group3:350*0.018=6.3 →6

Group4:350*0.086375≈30.231 →30

Group5:350*0.08375≈29.3125 →29

Group6:350*0.047132≈16.496 →16

Group7:350*0.410118≈143.541 →144

Wait, let’s sum these rounded numbers:

62 +62 +6 +30 +29 +16 +144 = 349. Hmm, we’re missing one representative. The total should be 350. This is due to rounding errors. The largest remainder method would adjust the group with the highest decimal part. Let’s check the decimal remainders:

Group1: 0.34375

Group2:0.775

Group3:0.3

Group4:0.231

Group5:0.3125

Group6:0.496

Group7:0.541

The decimals after the initial rounding are as above. The largest remainder is Group2 (0.775), then Group7 (0.541), then Group6 (0.496), then Group1 (0.34375), Group5 (0.3125), Group3 (0.3), Group4 (0.231). Since we need one more to reach 350, we add 1 to the group with the highest remainder, which is Group2. So Group2 would go from 62 to 63, making the total 350. Let’s check:

62 (Group1) +63 (Group2) +6 +30 +29 +16 +144 = 62+63=125; 125+6=131; +30=161; +29=190; +16=206; +144=350. Perfect.

But wait, in my initial calculation, Group7 was rounded up to 144 from 143.541, which is a remainder of 0.541. Group2’s remainder was 0.775. So when distributing the remaining seat, Group2 has the highest remainder, so it should get the extra seat. But in the initial rounding, Group7 was already rounded up, which might have taken that extra seat. Let me double-check:

Original unrounded numbers:

Group1:62.34375 →62, remainder 0.34375

Group2:61.775 →61, remainder 0.775

Group3:6.3 →6, remainder 0.3

Group4:30.231 →30, remainder 0.231

Group5:29.3125 →29, remainder 0.3125

Group6:16.496 →16, remainder 0.496

Group7:143.541 →143, remainder 0.541 (if we take floor initially, but I rounded to 144, which may have caused confusion).

Wait, perhaps I should first take the integer parts by flooring and then distribute the remaining seats based on the largest remainders. Let’s recast the problem properly.

The correct method is:

1. Calculate the exact number of representatives per group (decimal).

2. Assign each group the integer part (floor).

3. Sum the integer parts, which will be less than 350.

4. The remaining seats are distributed one by one to the groups with the largest fractional remainders.

Let’s apply this method properly.

Exact representatives:

Group1:62.34375 → floor 62, remainder 0.34375

Group2:61.775 → floor 61, remainder 0.775

Group3:6.3 → floor 6, remainder 0.3

Group4:30.231 → floor 30, remainder 0.231

Group5:29.3125 → floor 29, remainder 0.3125

Group6:16.496 → floor 16, remainder 0.496

Group7:143.541 → floor 143, remainder 0.541

Sum of floors:62+61+6+30+29+16+143= 62+61=123; +6=129; +30=159; +29=188; +16=204; +143=347. So total is 347, needing 3 more seats.

The largest remainders are:

Group2:0.775 (1st)

Group7:0.541 (2nd)

Group6:0.496 (3rd)

Group1:0.34375 (4th)

Group5:0.3125 (5th)

Group3:0.3 (6th)

Group4:0.231 (7th)

So the three largest remainders are Group2, Group7, Group6. Therefore, we add 1 seat to each of these groups:

Group2:61+1=62

Group7:143+1=144

Group6:16+1=17

Now the total is 62+62+6+30+29+17+144= Let’s calculate step by step:

Group1:62

Group2:62

Group3:6

Group4:30

Group5:29

Group6:17

Group7:144

Sum:62+62=124; +6=130; +30=160; +29=189; +17=206; +144=350. Perfect.

So the correct allocation is:

1. China:62

2. India:62

3. Russia:6

4. Europe (excl. ES/PT):30

5. Group5:29

6. Group6:17

7. Rest of the World:144

Wait, but in the initial approach, I had rounded Group7 up to 144, but according to this method, it’s the proper way. The confusion arose because initially I rounded some up and others down, which isn’t the correct method. The correct approach is to floor all and then add the remaining seats to those with the highest remainders.

Therefore, the final allocation should be as above. Let me confirm the numbers again:

Group1:62

Group2:62

Group3:6

Group4:30

Group5:29

Group6:17

Group7:144

Sum:62+62=124, +6=130, +30=160, +29=189, +17=206, +144=350. Correct.

This makes sense. Now, to ensure the populations are accurate. Let me double-check the population numbers used:

– China: 1.425 billion (correct as of 2023 estimates)

– India: 1.412 billion (similar)

– Russia: ~144 million (yes)

– Europe total is tricky. Europe’s total population is about 748 million. Spain is ~47 million, Portugal ~10 million, so subtracting those gives 748 – 57 = 691 million. Correct.

Group5: Spain+Portugal (57 million) + Mexico (~129m) + Central America (~50m) + South America (~434m). Total 57+129=186, +50=236, +434=670 million. Correct.

Group6: USA (~339m) + Canada (~38m) + Greenland (~0.056m) ≈377.056 million. Correct.

Group7: 8,000 – (1,425+1,412+144+691+670+377.056) = 8,000 – 4,719.056 = 3,280.944 million. Correct.

Therefore, the calculations are based on accurate population data. The method applied is the standard proportional allocation using the largest remainder method to handle rounding, ensuring the total is exactly 350.

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