Alex has 12 friends and 63 coins. what is the minimum number of additional coins he needs so that he can give each friend at least one coin and no two friends receive the same number of coins?

15 coins

Step-by-step explanation:

Alex has friends = 12

He has total coins = 63

Now,  if he want to add minimum number of coins in his coins for distribution,

The difference in the number of coin must be same or minimum,

The minimum difference between number of coins his friends can get =  1,

Minimum number of coin one person can get = 1,

Therefore, the order of coin that having minimum sum,

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

Total sum of this AP = 78

Thus, the minimum coins he can give all of his 12 friends = 78

Since, 78-63 = 15

⇒ The minimum number of additional coin = 15

not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove. 

an inaccurate proof leads to errors, or stating results that are not accurate.  which wil mess the probelm up you dont want this