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9966 [12]
2 years ago
10

A researcher plans to identify each participant in a certain medical experiment with a code consisting of either a single letter

or a pair of distinct letters written in alphabetical order. What is the least number of letters that can be used if there are 12 participants, and each participant is to receive a different code?
Computers and Technology
1 answer:
trapecia [35]2 years ago
5 0

Answer:

5 Letters

Explanation:

So we need 12 distinct codes made of a single letter or a pair of letters.

What would be the least number of letters?

Lets try with 3 letters A, B and C

The possible combinations are: A, B, C, AB, AC, BC

These are 6 codes and we need 12 so lets try more A, B, C and D

The possible combinations are: A, B, C, D, AB, AC, AD, BC, BD, CD

These are 10 codes and we need 12 so lets try more A, B, C, D and E

The possible combinations are:

A, B, C, D, E, AB, AC, AD, AE, BC, BD, BE, CD, CE, DE

Finally we got 15 distinct codes which are more than 12 so the least number of letters needed are 5.

Using formula:

Four letters = 4C1 + 4C2 = 4 + 6 = 10

Five letters = 5C1 + 5C2 = 5 + 10 = 15

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#include <iostream>

#include <string>

using namespace std;

void initializeArrays(string names[], int scores[], int size);

void sortData(string names[], int scores[], int size);

void displayData(const string names[], const int scores[], int size);

int main()

{

   string names[5];

   int scores[5];

   //reading names and scores

   initializeArrays(names, scores, 5);

   //sorting the lists based on score.

   sortData(names, scores, 5);

   //displaying the contents of both arrays

   displayData(names, scores, 5);

 

  return 0;

}

void initializeArrays(string names[], int scores[], int size){

   for(int i=0; i<size; i++){

       cout<<"Enter the name for score #"<<(i+1)<<": ";

       cin >> names[i];

       cout<<"Enter the score for score #"<<(i+1)<<": ";

       cin >> scores[i];

       }

}

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       int temp = 0;

       string tempStr = "";

       

       for(int i=0; i < size; i++){

               for(int j=1; j < (size-i); j++){

                      //checking max score and sorting based on it.

                       if(scores[j-1]< scores[j]){

                               //swap the elements!

                           //swapping scores

                               temp = scores[j-1];

                               scores[j-1] = scores[j];

                               scores[j]=temp;

                               

                               //swapping names

                               tempStr = names[j-1];

                               names[j-1] = names[j];

                               names[j]=tempStr;

                       }

                       

               }

       }

}

void displayData(const string names[], const int scores[], int size){

   cout<<"Top Scorers:"<<endl;

       //printing the elements up to the size of both arrays.

       for(int i=0; i<size; i++){

           cout<<names[i]<<": "<<scores[i]<<endl;

       }

}

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