A forum for good logic/math puzzles.

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Postby Jayraj » Thu Nov 01, 2018 6:15 pm UTC

You managed to identify the poisoned canister, and everyone was able to fill their bellies with chicken and juice.

After some well-deserved rest, you now explore your surroundings and find the radio equipment you were looking for.

Somehow there is no power in the whole installation, and you set out to find how to restore it.

You find a panel with 15 slots in a 3x5 format, and a set of 15 identical cables lying just beneath it.

The panel is numbered, but there is no numbering on the cables so you cannot match them in the correct slot.

Fearing that just plugging in cables at random might damage the equipment and your only chance at contacting the outside world, you decide to follow the cables to its source.

The search leads you outside where you decide to take the truck to continue not knowing how far you might have to go.

You finally arrive at a hydro power plant where the cables are connected to an identical panel as the one at the outpost.

Going inside you find a lever on an 'off' position and labeled "MAIN POWER".

You jump from joy and grab the lever and start to lift it up… a sudden realisation hits you and you let go of the lever slowly.

The power cables at the outpost were lying on the ground naked, what if turning the power on now would cause a short-circuit?

You realise that you will need to connect all the cables before turning on the power.

Going back outside to the panel and cables, you realise that while cables are indistinguishable from each other, it is possible they are not of the same resistance.

This means you will have to identify each cable on both sides to make the correct connections.

You only have a pen and lots of band aids, but searching the plant, you find a drone with broken propellers.

Dismantling the drone yields its power source and one functioning motor.

You go back to the truck and note that your fuel will only last for a few more trips.

Thanking your stars that you could save so much fuel on your way up, you begin to think strategically.

What is the minimum number of trips you need to restore power to the outpost, and how?

Note that the power source is powerful enough to activate the motor through the length of wires.

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Re: Power

Postby jaap » Fri Nov 02, 2018 7:04 am UTC

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Re: Power

Postby bjazz » Wed Nov 07, 2018 9:22 pm UTC

jaap wrote:http://forums.xkcd.com/viewtopic.php?t=12330

I came up with a solution before looking at this link. The linked problem is slightly different in that it takes polarity into account, but I can't tell if that makes a difference. Incidentally my solution was similar to what was proposed in the solution thread for that link in that I assumed you could bundle cables together and then test each one with the power and battery. Unlike the linked problem, I did not assume I needed 2 wires at the correct polarity - just a single connection between power and motor would give a signal. Are these correct assumptions?
At the hydro panel, mark all the cables with their place in the panel (#1 through #15), then remove all but #1. Splice cables #2 and #3 together into a 2-cable bundle, call this bundle “A”. Splice #4,5 and 6 into a 3-cable bundle, call it “B.” Splice #7,8,9 and 10 into a 4 cable bundle, “C,” and splice #11,12,13,14 and 15 into a 5-cable bundle called “D.”
Now, drive to the radio panel. From this end you should be able to energize one cable and measure voltage (using the motor) in either 0,1,2,3, or 4 other cables. Test each cable to find out which ones are bundled together. The one cable that doesn't energize any others is the #1 that you left in the panel (go ahead an plug that one in). For the others, mark them according to how many other cables they are bundled to (so you'll end up marking 2 cables with a "A", 3 cables with a "B", 4 cables with a "C" and 5 cables with a "D")
Next, still at the radio panel, rearrange the splices: splice one of each cable marked with a D, C, B, and A into a 4-cable bundle. Next splice a D, C, and B into a 3-cable bundle. And a D and C into a 2 cable bundle. And leave one each of A, B, C, and D unspliced.
Drive back to the hydro station and test each end, marking which group they are in. You will now be able to uniquely identify the cables and make a list to take back to the radio panel.
For example, go to bundle “A” containing cables #2 and #3. One of them will be unconnected, one will be part of a 4-cable bundle. Say if #2 was unconnected and #3 was in a 4-cable bundle. Make a note of it, then when you go back to the radio panel, plug the unconnected A into #2 and the A from the 4-cable bundle into #3. Each other bundle can be sorted this way.
Restore the connections to the hydro panel. Go back to the radio panel with your list, plug in all those connections, then one final round trip to the hydro panel to flip the main power switch.

So starting at the hydro plant, that's 1 round trip to determine the correct cables, then another round trip to plug in the correct wires at the radio and return to hydro to turn on the power, then one last 1 way trip back home to the radio. So, 2.5 round trips.

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