Plate Spotting
I was in my car crawling along the M6 motorway a few weeks ago, thinking that it would be quicker to walk to the exhibition I was attending, when I noticed a line of four cars on the lane next to me with number plates starting with J, K, L and M and ending in the same letters, though each car did not necessarily start and end with the same letter.
The car with L as the last letter was not next to the car with L as its first letter but was next to the one with J as the first letter.
What were the start and end letters of each of the number plates and what order were they in?
There is just a need to be systematic here. Try taking the information in a different order, starting with facts that have the least number of possibilities. For example the fact about number plates with M only has two possible outcomes.
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."