Red Billiard
please can you help me with two maths probelm solving question (pretty easy questions)?
1) colonel mustard is pracitsing his snooker in the billiard room.
how many triangular arrangments of balls ( there must be more than 1 ball in the arrangment) are there in this rack of red snooker balls ??? (there are 15 red snooker balls)
2) in the library there is a five volume set of books: ‘the use of lead piping in modern plumbing’, volumes 1-5, arranged in ascending order on the shelf. a bookworm eats its way from the front cover of volume 1 to the back cover of volume 5. if each volume is 3cm thick, how far had the the bookworm travelled ???
and please include your working out as well as the answer, thanks 
x
Not exactly a mathematical solution.
A B C D E
..F G H I
…J K L
….M N
……O
Triangles with 3 balls ABF BCG CDH DEI FGJ GHK HIL JKM KLN MNO KMN JKG KLH FGB GHC HID (16)
Triangles with 6 balls ABCFGJ BCDGHK CDEHIL FGHJKM GHIKLN JKLMNO JKLGHC (8)
Triangles with 10 balls ABCDFGHJKM BCDEGHIKLN FGHIJKLMNO (3)
Original Triangle 15 balls (1)
16 + 8 + 3 +1 = 28 Triangles.
Since the books are arranged in ascending order and we must assume they are all the same way up the bookworm will have eaten its way through all of the books except volume 1 that is 4 x 3cm = 12cm.
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