First of all, it’s important to establish that all of the rows are isolated from one another. A prisoner’s decision to flip the switch (or leave it off) does not affect anyone outside his/ her row.
Now let’s look at all the possible outcomes for each row. Prisoners highlighted in green received no shock, prisoners highlighted in yellow received a moderate shock, and prisoners highlighted in red received a severe shock.
If NONE of the prisoners flipped the shock switch, then none of them got shocked.
If SOME (not all) of the prisoners in a row flipped the shock switch, then a moderate shock is administered to the prisoners in the row who left their switches off.
If ALL of the prisoners in a row flipped the shock switch, then they ALL received severe shocks.
Let’s break down the possible fates of each individual prisoner:
A prisoner who turned his switch ON will receive…
– NO SHOCK if anyone else in his row left his switch off.
– A SEVERE SHOCK if everyone else in his row turned their switches on.
A prisoner who left his switch OFF will receive…
– NO SHOCK if nobody else in his row turned their switches on.
– A MODERATE SHOCK if anyone else in his row turned their switch on.
Now that we’ve explained that, let’s begin…
The beginning board:
1. Amy’s hint states that she received a shock, but Kirsten did not. Thus, we can draw two conclusions:
– Someone else in her row used the switch.
– The prisoners in her row who did use the switch received no shock, and the prisoners who didn’t received a shock.
Since Kirsten did not get shocked, she must have turned her switch on.
2. There’s only one other prisoner in Kirsten’s row who avoided getting shocked, and it’s not Vincent (since he’s not adjacent to Kirsten). He must have left his switch off.
3. Vincent’s clue tells us that Judy and Zosia chose the same option. So they either both decided to turn their switches on, or they both decided to leave theirs off.
If Judy and Zosia both turned their switches on, then at least one of Evelyn, Omar and Umberto would have been shocked. Any one of them who decided to leave the switch off would receive a moderate shock, and if they all turned their switches on, then everyone in the row would receive a severe shock.
However, according to Amy’s clue, neither Evelyn nor Omar nor Umberto received any shock, so Judy and Zosia can’t have turned their switches on. Thus, they left them off.
4. There is only one person adjacent to Judy who got shocked. We know it can’t have been Ingrid, Evelyn or Omar (Amy’s clue), so it was either Derek or Norah (but not both).
This means that at least one person in Row 4 turned the switch on, so anyone in Row 4 who left the switch off got shocked. Ingrid didn’t get shocked (again, see Amy’s clue), so her switch must have been on.
5. Yaakov is in Row 4 and he didn’t get shocked, so he must have turned his switch on.
6. Look at the possible scenarios outlined on the first page. A prisoner can’t have received a severe shock unless everyone else in his row received one too (which would mean that everyone in the row turned the switch on).
So all the prisoners in at least one row used the switch. But which one(s)?
In Rows 1, 4 and 5, there’s at least one prisoner who left the switch off, so we can rule those out immediately. That leaves us with either Row 2 and Row 3 (or both).
Ingrid’s clue let us know that she’s adjacent to three criminals who used their switches. If everyone in Row 3 received the severe shock, then Carl, Helen and Murphy must have all used their switches.
But that can’t be true. We know that of Derek and Norah, one received a shock while the other didn’t (Judy’s clue), so one of them had to have turned the switch on. So Carl, Helen and Murphy can’t have all used their switches, since that would make Ingrid adjacent to at least four switch users.
Therefore, we can rule out Row 3 and we’re only left with Row 2. Blake, Greg, Larry, Rudy and Winston all turned their switches on.
7. According to Larry’s clue, the number of shocked prisoners in Row 3 was odd; either 1, 3 or 5.
– It can’t have been five (see Ingrid’s clue)
– It can’t have been three, either. According to Kirsten’s clue, there’s only one other prisoner in her row who didn’t get shocked. That means that of the two remaining prisoners in the row (Frank and Percy), one received a shock while the other didn’t. Since we already know that Amy and Vincent got shocked, that means that a total of three prisoners in Row 1 got shocked. But according to Blake’s clue, no two rows have the same quantity of shocked prisoners.
– So one prisoner in Row 3 got shocked.
That means that there was one person in Row 3 who left the switch off. It’s too early to tell who it is, but we do know that it can’t have been Steve or Mr. X. If it was either of them, then Carl, Helen and Murphy must have turned their switches on, and as previously established by Ingrid’s clue, that isn’t possible. Both Steve and Mr. X turned their switches on.
8. Of the remaining three prisoners in Row 3 (Carl, Helen and Murphy), two used their switches while one did not.
With this information, we can start to determine who the three switch users adjacent to Ingrid are. Two of them are in Row 3 (since Ingrid is adjacent to Carl, Helen and Murphy), and the last remaining one is either Derek or Norah. Outside of those two groups, Ingrid isn’t adjacent to anyone else who used the switch. Thus, Evelyn and Omar left their switches off.
We also know that Evelyn and Omar did not get shocked (Amy’s clue), so nobody else in their row could have turned the switch on. Umberto left his switch off.
– We know that Blake, Greg, Larry, Rudy and Winston all received severe shocks. That’s five.
– Amy and Vincent were shocked, too, and from Kirsten’s clue, we can determine that either Frank or Percy got shocked. That’s eight.
– As we previously established, exactly one prisoner in Row 3 got shocked. That’s nine.
– From Ingrid’s clue, we know that either Derek or Norah got shocked, but not both. That’s ten.
That leaves us with one remaining prisoner; Terrance. He got shocked, which means that he left his switch off.
10. Look at Zosia’s clue again. There’s exactly one other prisoner in his diagonal who received no shock. It wasn’t Amy, Greg or Terrance, so it must have been Murphy. He did not receive a shock, and since Steve and Mr. X both turned their switches on, Murphy must have turned his on as well.
We know that Murphy, Steve, Mr. X, Yaakov, Zosia, Umberto, Omar did not receive shocks, so Norah must have, which means that she left her switch off. This, in turn, means that Derek turned his on.
12. Helen can’t have been zapped because her option had to have been different from Frank’s. Helen turned her switch on, Frank didn’t, Percy did, and Carl didn’t.