An evil idea came to my mind. I promise you I won't use it :-D
Today online I've seen sort of a test:
- Stole from a shop: 10 points
- Had a threesome: 20 points
- Cheated on a girlfriend: 15 points ...
One is supposed to sum all of his points and post a sum he/she's got for fun.
And here I thought... What if it is possible to make up a number of such weights so that for variables that only can be either 0 or 1 equation would have only ONE solution for any sum that can be acquired?
I mean, from the example above, 10*x+20*y+15*z+...=SUM would have only one solution for x,y,z from [0, 1].
How would you search that 10, 20, 15,... coefficient list?
Been thinking about it for like 3 hours already. It consumes me :-)
Don't suggest something like "powers of X" weights or "use prime numbers and multiplication instead of sum", it is kinda too easy to understand :-)
EDIT: also, for "powers of X" weights would differ way too much, so it wouldn't look okay, that would raise suspicions for potential victim :-)
If your reason to forbid powers of 2 is that the coefficients are too obvious, you can always add a larger power of $2$ to all the coefficients. For example, if you have 4 coefficients, you just choose $$2^A+2^0\ ,\ 2^B+2^1\ ,\ 2^C+2^2\ ,\ 2^D+2^3$$
where $A$, $B$, $C$, $D$ are any integers greater or equal to $4$ (number of coefficients), possibly repeated. In this way, you can choose for example
$$33x+ 18y+ 20z+ 40t$$
where I set $A=D=5$ and $B=D=4$. Those numbers look less obvious than powers of $2$.
You can extend this to higher bases, optionally with additional multiplying factors smaller than the base (i.e., $2\cdot 3^A$, etc.).
With these methods, you can still easily read off the $(x, y, z, t)\in[0,1]$ unknowns from the last digits of the binary (or higher-base) representation of the result.