"We have a 50% chance to solve it right here," I explained. "And even if it won't work, we'll know for sure which way to dig."
"But the leak isn't here, and we still don't know where it is!" exclaimed the pool guy.
"We assume that it's on this pipe, right?"
"Yes, we do," he said.
"We also assume that this pipe is an 'appendix', right?"
"The rest is just logic. We have four possibilities here:
1. The pipe connects to the water system on the left, under the pool, and the leak is on the right.
2. The pipe connects to the water system on the right, under the pump station, and the leak is on the left.
3. It connects on the left, and the leak is on the left.
4. It connects on the right, and the leak is on the right.
If it's 1 or 2, we'll fix it here. If it's 3 or 4, we'll know where to dig."
"But - how?"
"Bear with me. Would you please seal the outlets inside the pool again?"
"No problem." It was done in five minutes.
"Now, cut this pipe."
"Yes, right through. Into two. Separate the left from the right."
"I hope you know what you're doing. You're the boss," he said visibly confused. However, in five minutes that was done, too. Water ran out from the two parts for a while and stopped.
"Look, the water is milky!" I pointed. "It's a good sign. This supports our theories so far. Your miracle stuff got into this pipe, but didn't flow though it. It is an appendix, and it is connected to the water system somewhere!"
"We still don't know where, or where the leak is."
"Soon, soon," I replied. "Could you open the outlet inside the pool for a few seconds, and then seal it again?"
"Sure." He did. A little stream of water came out from the left part of the cut pipe.
"It's either 1 or 3!" I exclaimed. "The water comes from the left. Seal the left part of the cut now, would you?"
"Oh, I see," smiled the pool guy. In 15 minutes that was done.
"You will call me tomorrow, right?" he said. "And you will tell me if it's case 1 or case 3. Good luck."
He opened the outlets inside the pool and left. Twenty-four hours later, the water level in the pool had dropped just half a centimeter.
"Come and cover that hole in the ground." I told the pool guy. "How much do I owe you?"
"You paid for all the wasted water while I learned a whole new perspective from you. No charge. It was my pleasure."