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Plate Spotting

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Grace, from Nottingham Girls High School, and Clement, from River Valley High School, managed to crack this problem. Well done to you both.

Clement tackled it in this way:

"Since the car ending with L was NOT beside the one starting with L, but was next to the one that started with J, we get these possibilities:

**** L*** L*** L*** J*** **** ***L ***L
L*** **** **** J*** ***L ***L J*** J***
J*** J*** ***L ***L **** J*** L*** ****
***L ***L J*** **** L*** L*** **** L***

Since the two cars with M on their plates were at opposite ends of the group, we get these possibilities:

***M L**M L**M M*** M**L M**L
L*** **** J*** ***L J*** J***
J*** J*** ***L J*** L*** ****
M**L M**L M*** L**M ***M L**M

Since the car whose license plate ended in K had the one starting with L in front, we get:

***M L**M L**M
L*** ***K J**K
J**K J*** ***L
M**L M**L M***

Since the car with a plate starting with K was not next to the one starting with an L, we get:

L**M
J**K
K**L
M**J

Therefore this is the order of the cars."