Here's a riddle: Three men check into a hotel and are told the room is $30; they each contribute $10. (It's an old riddle; change it to 300$/100$ is that makes you happy.) The hotel manager later realizes that they room is only $25, so he gives $5 to the bellhop and tells him to return it to the men. The bellhop figures that giving three men $5 to split will only cause a fight, so he pockets $2 and returns the other $3 to the men. Now here's the thing: Each man paid (10 - 1)$ = 9$ for the room; that's a total of 27$. Add to that the $2 in the bellhop's pocket and you have $29. Hmm... where's the missing dollar? We'll come back to this in a moment. (Or more; depends on how fast your read, now, doesn't it?)

The gemara (Bava Kama 53a) discusses the distribution of blame (ie, how much it will cost each of the participants) when Reuvein's ox pushes Yehuda's ox (Ferdinand) into Levi's pit and Yehuda's ox subsequently dies. The gemara brings two opinions, both attributed to R' Nachman. One opinion is that Reuvein and Levi each pay Yehuda half the value of his ox. The other opinion is that Reuvein pays 75% and Levi owes the other 25%. The resolution is easily resolved: The first opinion is a case where Reuvein has been warned about the violent behavior of this ox three (or more) times already; meaning that Reuvein is culpable for 100% of any further damage caused by his ox. Hence, since Reuvein and Levi are equally culpable, they share equally the cost of any damage they jointly caused. The second opinion is a case where Reuvein's ox is a regular ol' innocent ox; maybe he wasn't watching where he was going, maybe a bee stung him. In that case, of course, Reuvein is only culpable for half the damages his regular ol' innocent ox inflicts. That's where we get the 75/25 percent split. Now the fun starts.

The gemara lodges a strong complaint against R' Nachman's opinion. Let's say they are both individually responsible for the whole debt. In that case Reuvein only owes 50%, since his ox is an innocent little lamb, and Levi owes 50% because Yehuda doesn't get a profit on this deal. Let's try the other possibility: each is culpable for half of the damages. In that case Levi pays his half and Reuvein pays on 25% (half of his half of the damages), and Yehuda loses 25%; so sorry. Any way you slice it, 50/50 or 50/25, there is no 75/25 split here.

Let's think this through. Philosophically either of them -- Reuvein's ox or Levi's pit -- could have killed Yehuda's ox by itself. Also, again philosophically, if Reuvein's ox hadn't pushed or if Levi's pit hadn't been there, then maybe Yehuda would still have Ferdinand. But it did and it was and Ferdinand is now meat. R' Nachman, says the gemara, was a dayan/judge. Deciding who pays what damages is not philosophy for him; it is day and and day out, rubber hits the road, pedal to the metal real life.

Let's revisit the riddle. The answer is that there is no such thing as 25$ + 2$; the correct analysis says each paid 9$, which is 27$, of which 25$ went to the hotel and 2$ went into the bellhop's pocket. It's similar here. If they are both fully culpable, then why did you charge Reuvein first? That makes him pay the same even though the Torah says he gets a break. Really, then, Reuvein pays 50% and Levi pays 100%, but since Yehuda only get 100%, the extra 50% is (Torah) rebated back to them equally; hence (100-25)/(50-25) = 75/25. What about the other perspective (the 50/25 one)? Yehuda can say to Levi, "I am awfully sorry that Reuvein only wants to pay 25%, but my poor Ferdinand was found dead in your pit. As far as I am concerned, you are the only one who owes me anything. If you can recoup some of your loss from Reuvein, more power to you!" Hence, (50 + 25)/25 = 75/25.

And you thought you'd never use that high school algebra.

The gemara (Bava Kama 53a) discusses the distribution of blame (ie, how much it will cost each of the participants) when Reuvein's ox pushes Yehuda's ox (Ferdinand) into Levi's pit and Yehuda's ox subsequently dies. The gemara brings two opinions, both attributed to R' Nachman. One opinion is that Reuvein and Levi each pay Yehuda half the value of his ox. The other opinion is that Reuvein pays 75% and Levi owes the other 25%. The resolution is easily resolved: The first opinion is a case where Reuvein has been warned about the violent behavior of this ox three (or more) times already; meaning that Reuvein is culpable for 100% of any further damage caused by his ox. Hence, since Reuvein and Levi are equally culpable, they share equally the cost of any damage they jointly caused. The second opinion is a case where Reuvein's ox is a regular ol' innocent ox; maybe he wasn't watching where he was going, maybe a bee stung him. In that case, of course, Reuvein is only culpable for half the damages his regular ol' innocent ox inflicts. That's where we get the 75/25 percent split. Now the fun starts.

The gemara lodges a strong complaint against R' Nachman's opinion. Let's say they are both individually responsible for the whole debt. In that case Reuvein only owes 50%, since his ox is an innocent little lamb, and Levi owes 50% because Yehuda doesn't get a profit on this deal. Let's try the other possibility: each is culpable for half of the damages. In that case Levi pays his half and Reuvein pays on 25% (half of his half of the damages), and Yehuda loses 25%; so sorry. Any way you slice it, 50/50 or 50/25, there is no 75/25 split here.

Let's think this through. Philosophically either of them -- Reuvein's ox or Levi's pit -- could have killed Yehuda's ox by itself. Also, again philosophically, if Reuvein's ox hadn't pushed or if Levi's pit hadn't been there, then maybe Yehuda would still have Ferdinand. But it did and it was and Ferdinand is now meat. R' Nachman, says the gemara, was a dayan/judge. Deciding who pays what damages is not philosophy for him; it is day and and day out, rubber hits the road, pedal to the metal real life.

Let's revisit the riddle. The answer is that there is no such thing as 25$ + 2$; the correct analysis says each paid 9$, which is 27$, of which 25$ went to the hotel and 2$ went into the bellhop's pocket. It's similar here. If they are both fully culpable, then why did you charge Reuvein first? That makes him pay the same even though the Torah says he gets a break. Really, then, Reuvein pays 50% and Levi pays 100%, but since Yehuda only get 100%, the extra 50% is (Torah) rebated back to them equally; hence (100-25)/(50-25) = 75/25. What about the other perspective (the 50/25 one)? Yehuda can say to Levi, "I am awfully sorry that Reuvein only wants to pay 25%, but my poor Ferdinand was found dead in your pit. As far as I am concerned, you are the only one who owes me anything. If you can recoup some of your loss from Reuvein, more power to you!" Hence, (50 + 25)/25 = 75/25.

And you thought you'd never use that high school algebra.

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