SOLUTION: Twenty girls stood in a row facing right. Four boys joined the row, but facing left. Each boy counted the number of girls in front of him. The numbers were 3, 6, 15 and 18 respec

Question 1133239: Twenty girls stood in a row facing right. Four boys joined the row, but facing
left. Each boy counted the number of girls in front of him. The numbers were 3,
6, 15 and 18 respectively. Each girl also counted the number of boys in front of
her. What was the sum of the numbers counted by the girls?
Answer by ikleyn(52805) (Show Source): You can put this solution on YOUR website!
.

It is easy.

From the condition (from the given data), you can restore the placement of the girls and the boys in the row, from left to right. 


It is as follows:


G1  G2  G3  B1  G4  G5  G6  B2  G7  G8  G9   G10   G11  G12  G13  G14  G15  B3   G16  G17  G18   B4  G19  G20  



Then the number of boys counted by each girl in front of she, is as follows:

G1  G2  G3      G4  G5  G6      G7  G8   G9   G10  G11  G12  G13  G14  G15       G16  G17  G18       G19  G20
4   4   4       3   3   3       2   2    2    2    2    2    2    2    2         1    1    1         0    0


So, the sum you are looking for is  4*3 + 3*3 + 2*9 + 1*3 + 0*2 = 42.


Now, having this solution before your eyes, it is not difficult to re-tell it in the compact form, by writing 
and justifying the last summation immediately, omitting all details that preceed.

Solved, answered, explained and completed.

RELATED QUESTIONS
7 boys and 6 girls sit in a row. What is the probability of having a boy at each... (answered by Edwin McCravy)

Calculate the number of ways in which three girls and four boys can be seated on a row of (answered by Edwin McCravy)

5 girls and 4 boys sit in a row. If only two boys sit next to each other , find the... (answered by Edwin McCravy)

A school teacher has 6 girls and 8 boys to arrange for a choir. Determine the number of... (answered by Edwin McCravy)

In how many ways can 3 boys and 2 girls be arranged in a row if a selection is made from... (answered by Edwin McCravy)

I think I know the answer but can't get the formula right. HELP!!! From a group of boys... (answered by josmiceli,checkley71)

From a group of boys and girls, 15 girls leave. There are then left two boys for each... (answered by ankor@dixie-net.com)

From a group of boys and girls, 15 girls leave. There are then left two boys for each... (answered by josmiceli)

A photograph of a diving team is to be taken with the team members in two rows. The team... (answered by math_tutor2020,greenestamps)