License Plate Number Problem

[pkrish]

Hi,

I am trying to solve a problem with 4 numbers on a license plate or rather 4 numbers.

Let's say there's a license plate with 4 numbers 3420

I need an output of 10 from these numbers. i.e. 3X4 - 2 = 10

Assumptions: All 4 numbers cannot be same and not all can be zero

You can sum the numbers. You can multiply two numbers and divide by one of the other numbers and subtract from the remaining 4th number.

I want to know what all permutations and combination can I use in my approach. Please let me know.

Thanks

[Perhaps check it again]

Your rules of what to do are vague.

And I don't think you mean "...and subtract FROM the remaining 4th number."

I think you don't mean for the word "from" to be in there.

You're talking about "digits," not "numbers."

The following sentence doesn't make sense and/or is redundant:

"All four numbers [read: digits] cannot be [the] same[.] and not all can be zero[.]"

A zero *is* already included in the first part of the sentence.

Supposedly these would be examples of yours:

4321 ----> 4 + 3 + 2 + 1 = 10

0505 ----> 0 + 5 + 0 + 5 = 10

8642 ----> (8 X 6)/4 - 2 = 48/4 - 2 = 12 - 2 = 10

[plasmid]

Are you asking us to find the number of different ways of performing operations on a set of four numbers? For example, if you were to label the four numbers on the plate A, B, C, and D, do you want us to enumerate how many possible ways there are to perform the operations on them, like

1) A+B+C+D

2) A+B+C-D

3) A+B-C+D

...

N) (A*B)/(C-D)

...

X) (A-C+D)/B

...

Or are you asking whether there's any way to guarantee that you can perform some set of operations to come up with 10 for any set of four numbers when they are not all the same?

[dgreening]

Attempt at restating the problem

for 4 digits, you are allowed to insert any math operators between the digits and assume there is an "= 10" at the end of the sequence.

so

9339, could be arranged as (93 - 3) / 9 = 10

8952 could be arranged as 8 + 9 + 5 - 2 = 10

The question is "is there a method, algorithm .... that will allow me to identify all the 4 digit sequences that fit this criteria?"

BTW, use of exponentials could create some interesting options.

[phil1882]

okay, so you want to exclude any sequences which don't allow you to = 10 after standard operations are preformed.

the only algorithm i know of that's guaranteed to work is to continually guess and check. until either a solution is found, or all possible operations have been tried.