Distance between (-7,-6) and (-2,-16)

Exact form:

2

Decimal form:

7.21110255 or 7.21

The celebrities on most intelligent list are 29 and 4 celebrities were on none of the list

Explanation:

According to the question,

Criteria 1:  6 were in all three categories  

Criteria 2:19 were placed into most powerful and most liked

Criteria 3:13 were on most powerful and most intelligent  

Criteria 4:10 were on most liked and most intelligent  

According to above data,  

1) In most powerful category

According to Criteria 1, 2 and 3

Total no of celebrities in powerful category = 6+19+13 = 38

No of celebrities left in this category = 45 – 38 = 7

2) In most liked category

According to Criteria 1, 2 and 4

Total no of celebrities in most liked category = 6+19+10 = 35

No of celebrities left in this category = 35 - 35 = 0

3) In most intelligent category

According to Criteria 1, 3 and 4

Total no of celebrities in intelligent category = 6+13+10 = 29  

Therefore, the celebrities on most intelligent list are 29 and 4 celebrities were on none of the list as it is given that only 25 are in most intelligent list