[Guest]

On a particular bank cheque, the digits 0-9 are used but must be written like the display on a calculator.

 _       _   _       _   _  __   _   _

| |   |  _|  _| |_| |_  |_    | |_| |_|

|_|   | |_   _|   |  _| |_|   | |_|  _|

However, this is open to fraud. For example you can add lines to turn any digit into an '8'. A 4 can be turned into a 9 and so on. The bank wants to use a new set of digits, still numerically zero to nine, and still based on the 7 segment display. However, they must be designed differently so that it is impossible to alter a digit by adding lines. Hence, you will be unable to turn one digit into another.

Can you find such a set?

What is the largest set of digits possible with these restrictions?

(You do not have to worry about changes that may occur by removing lines)

Edited July 5, 2010 by psychic_mind

[Guest]

make each digit the same amount of lines, for example each digit would have exactly 5 lines so you'd have:

 _   _    _         _    _

|_|  _|  |    | |  | |  |_|

|    _|  |_|  |_|  | |   _ 

For largest set possible, the current number I can think of is 35 (with the technique in the spoiler using 3 or 4, both are same) but there might be another way which you can achieve more, I'll think of it later...

Edited July 5, 2010 by Anza Power

[plainglazed]

Was thinking similarly to Anza

expected 7C3 or 7C4, both equal to 35, might be the max

EDIT: switched numbers in haste

EDIT: oops, yeah. now, I see where Anza's coming from. Had just checked out his spoiler at first.

Edited July 5, 2010 by plainglazed

[Guest]

join all the distanced lines,for eg,7,5 etc,any additional line added would depict overwriting of digits at a point ,the begn. and end of the inserted line.it can be detected when the cheque scanned by OMR

[Guest]

do you have to worry about a number being able to be changed to a lower number? eg. 7 -> 3

[Guest]

do you have to worry about a number being able to be changed to a lower number? eg. 7 -> 3

Yeah, you need that numbers wouldn't be changed at all for either bigger or smaller...

I think the max is 35 and I have proof:

You make a number system for instance which all numbers are from 4 out of 7 lines (3 lines is the same because you can invert all the numbers) if you want to add to the system numbers with more lines, like a 5-liner number, you have from the 4-liner numbers more than one that can be added to and be made into the new number (5 to be exact), if you want to add to the system a number of lesser lines, like for instance a 3-line number, in that number there are 4 places where you can add a line and convert it into a 4-line number, so you'd add one number but have to give up on 4 others, so the only and best way to do it is for all numbers to be the same amount of lines...

Edited July 6, 2010 by Anza Power