\begin{matrix} a = 12 & b = 6 & c = 5 & d = 1 & e = 0\\ \end{matrix}
How can I create a fun puzzle or word problem that would arrive at this solution above?
For example,
$$a+b+c+d+e=24$$ "$A$ is twice as large as $B$"
"$B$ is one larger than $C$"
From the $3$ statements above, we can generate: $$a=2b$$ $$c=b-1$$
Substitution: $$2b+b+(b-1)+d=24$$ $$4b+d=25$$
So, do I necessarily need to have a $3$rd clue that relates $b$ and $d$ ?
Like "$B$ and $D$ add up to $7$" Or "$B$ is $6$ times larger than $D$" ?
Any other ways to approach this?
Normally, you need five equations for five unknowns. "Fun" is not a mathematical concept, but is important in puzzles. If you just give five sentences that represent the five equations needed, it is unlikely to be a fun puzzle. Usually you need to conceal (one of) the equations so the reader doesn't see it immediately, or have some other condition that substitutes for one. An example would be the children's ages problem, where there is a mention of "the oldest". That tells you there is a unique oldest, which is the key to the puzzle.