Something Feminine
Five girls --Alicia, Brenda, Cheryl, Desiree, and Eve-- are standing in a row. Each of them has a different number of hairclips -- 0, 1, 2, 3 and 4 -- worn on their head.
-
Immediately to the left of Desiree is a girl with 2 hair clips.
-
Cheryl is immediately to the left of the girl without hair clips.
-
The girls on the left three positions combined have the same number of hairclips as the girls in the right two positions combined.
-
The girl right in the middle has an odd number of hair clips.
-
The girl on the extreme right has an even number of hair clips.
-
Eve is standing at one of the ends.
-
The number of hair clips that Alicia has is a perfect square. The number of hair clips on the other four girls combined, is also a perfect square.
How many hair clips does Brenda have?
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Observe that the five girls have 10 hairclips in all. For fact 7 to be true, the only possibility is Alicia has one hairclip while the other four girls have a total of nine. Fact 3 means the left three girls have five hairclips in total while the right two girls also have five hairclips in sum. This means the girl with no hairclips must belong to one of the left three positions since no girl has more than four hairclips. From fact 2, the girl without hairclips can't be on the extreme left as there is no girl to her left. From fact 4, she can't be in the middle too as zero is an even number. So she must be second from the left.
Fact 2 means Cheryl is on the extreme left. From fact 1, the girl on the extreme right cannot have two hairclips as there as no girl to her right. She also cannot have zero hairclips. The only possible even number (see fact 5) would be four. It follows that the girl fourth from the left has 5-4=1 hairclip. That girl must be Alicia. Also, from fact 6, since the leftmost girl is Cheryl, the rightmost girl who has four hairclips is Eve.
Between the leftmost and middle girl, the one with two hairclips is on the extreme left or Cheryl while the girl with three is in the middle (see fact 4). This means Desiree is second from the left. Brenda has to be in the middle with three hairclips!