Numbered cars
Can you crack my code and use it to find out what two car number plates add up to?
Problem
I was looking at the number plate of a car parked outside my house - S208VBJ. Using my special code S208VBJ adds to $65$.
They all also add to $65$ using my code!
Using the code you treat every character, that is a digit or a letter, as separate.
Numbers are simply added together so that, in the first number plate $208$ is $2 + 0 + 8 = 10$.
Letters are translated into numbers in an organised and systematic way. That means that if you know the value of F and H you not only know the value of G, but can easily work out all the rest of the alphabet.
Can you crack my code and use it to find out what both of these number plates add up to?
Getting Started
Write down the alphabet.
The two number plates beginning with V might provide a useful clue.
What is the most obvious way of turning letters into numbers? Vary it!
Student Solutions
Nicky from Westende Junior School approached this problem very logically. He wrote:
Subtract the value of the numbers from each of the five number plates.
So, for the illustrated car,
$2+0+8=10$ $65-10=55$ so S+V+B+J=$55$.And for the 4 other cars
$2+5+3=10$ $65-10=55$ so V+H+D+S=$55$
$5+1+6=12$ $65-12=53$ so R+J+S+H=$53$
$2+0+2=4$ $65-4=61$ so V+B+D+S=$61$
$9+6+8=23$ $65-23=42$ so T+H+T+R=$42$.Look at the letters on the two number plates beginning with V (VHDS & VBDS). There is only one letter different. The plate with H has a value 6 less than the one with a B, so that implies the alphabet has been written backwards as the numbers increase e.g.
$1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26$
Z Y X W V U T S R Q P O N M L K J I H G F E D C B ACheck this solution works for the $5$ number plates which add up to $65$. It does.
Use the code to find the value of the two new number plates:
T$584$YME and P$214$DOR both add up to $62$.
Excellent reasoning Nicky, although you were lucky you picked Z as $1$ to start with! Bronya from Tattingstone School used a similar method and noticed that it seemed to be that the closer the letter is to the beginning of the alphabet, the bigger the amount it is worth. She then tried A = $26$, B = $25$ etc as Nicky did.
Many of you read the clue and worked from there. Very sensible! Leila and Sheya from St Andrew's C of E Primary School in Totteridge told us:
First we tried A=$1$ B=$2$ C=$3$ and so on but that did not work.
Then we tried A=$2$ B=$3$ C=$4$ and so on but that did not work either.
The we tried the alphabet in reverse order A=$26$ B=$25$ C=$24$ and so on and that worked!
Then using the code we worked out the total of the bottom number plates:
T$584$YME=$7+5+8+4+2+14+22$=$62$
P$214$DOR=$11+2+1+4+23+12+9$=$62$
I wonder if you read the clue, girls?!
Teachers' Resources
Numbered Cars
I was looking at the number plate of a car parked outside my house - S208VBJ.
Using my special code S208VBJ adds to $65$.
They all also add to $65$ using my code!
Using the code you treat every character, that is a digit or a letter, as separate.
Numbers are simply added together so that, in the first number plate $208$ is $2 + 0 + 8 = 10$.
Letters are translated into numbers in an organised and systematic way. That means that if you know the value of F and H you not only know the value of G, but can easily work out all the rest of the alphabet.
Can you crack my code and use it to find out what both of these number plates add up to?
Why do this problem?
This problem practises working systematically on addition and subtraction. This is a code, not algebra, and learners will need to try things out as well as working them out, so using trial and improvement will be essential.
Key questions
Possible extension
Learners who found this problem easy could try Ishango Bone.
Possible support
Suggest starting by writing out the numbers on the number-plates and adding up each one. Then write out the alphabet and think of a way of varying A = $1$, B = $2$ etc.