Four bells, four strings, and a seemingly simple question. Before trying random combinations, it's worth asking yourself if the goal is even achievable.
The binary bells
Riddle statement
Four bells A, B, C and D start silently.
There are four strings:
- If they were silent, they start ringing.
Is it possible to make only bell C ring at the end? If you think so, indicate which ropes need to be pulled; If you think not, explain why.
Show solution
Solution
Answer: No, it is impossible.
The key is to look only at the bells A, B and C.
Each string changes between those three an even number of bells:
C: changes 2;
W does not ring any of A, B and C: changes 0.
Therefore, the parity of the number of bells ringing between A, B and C never changes.
At first 0 of those 3 bells ring, which is an even number. But “only C” would mean that in the end it sounds exactly 1 between A, B and C, which is odd.
That cannot happen.
So there is no string sequence that leaves only the C bell ringing.