Elie's Expositions

A bereaved father blogging for catharsis... and for distraction. Accordingly, you'll see a diverse set of topics and posts here, from the affecting to the analytical to the absurd. Something for everyone, but all, at the core, meeting a personal need.

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Tuesday, April 11, 2006

Two Torah Trivia By The Numbers

A couple of Torah-related numeric brain teasers appropriate for this time of year.

1) Here's one I heard from my Zaidah, A'H, concerning the upcoming Parshas Shmini, which was his bar mitzvah parsha exactly ninety years ago! The name of this parsha, which is read this year on the Shabbos right after Pesach, means "eighth". And in fact, in some years the first aliyah [portion] of Shmini is, in fact, read exactly eight times. How is this possible?

2) This one is original and, if I may say so myself, is my all-time favorite Torah brain teaser because it requires knowledge of algebra, halacha, and Hebrew grammar to get the one-and-only-one correct answer!

Beginning the second day of Pesach, we count the "omer", a forty-nine day period between Pesach and Shavous. The omer is counted in both days and weeks - e.g., "today is nine days, which are one week and two days in the omer".

Now there is exactly one day of the omer in which the Hebrew wording used for the day count and the week count are exactly parallel. To illustrate, here's a fake example: "hayom arba u'sheloshim yom, shehaym arba shavous u'shlosha yamim laomer". As illustrated by my color coding, the words used in the two phrases counting the days and the weeks respectively match up in order: arba and arba, shloshim and shlosha. Obviously, this example is fake because the 34th day of the omer is not four weeks and three days. But there is exactly one omer day where this does come out right!

Of course, the correct answer can be found by the brute force method of simply reading through each day (boo!) so in order to get this one right you have to show the math!

Have fun with these. I'll be on blog-cation until after the holiday. So a chag kasher v'samayach, a happy and kosher Pesach to all my Jewish readers. And to my gentile readers, just plain happiness!


At 4/12/06, 4:32 AM, Blogger Soccer Dad said...

I haven't figured out the first one and will leave it to a ba'al koreh.
23 that is 3 weeks and 2 days.

At 4/12/06, 11:35 AM, Anonymous Bruce Epstein said...

The first answer is if Pesach begins on Shabbat. We read Shmini the Shabbat mincha, Monday, and Thursday before Pesach, the two Shabbat minchas of Pesach, and the Monday, Thursday, and Shabbat morning after Pesach. This can only happen outside of Israel.

At 4/12/06, 12:09 PM, Anonymous trn said...

x + 10y = 7x + y
9y = 6x
3y = 2x => x=3, y=2 (Negative values are not applicable.)
The 3-and-20 (23rd) day is 3 weeks and one day.

At 4/12/06, 12:14 PM, Anonymous trn said...

The 3-and-20 (23rd) day is 3 weeks and one day.

Oops, I didn't finish that properly.

. . . and two days.

At 4/17/06, 6:04 PM, Blogger מיטוואך said...

k'shechal shmini* b'shmini** korim shimini*** shmonah p'amim.

*the eighth day of Pessach
**On the Shabbos we ought to have read Shemini
***the parshah

At 4/20/06, 11:50 PM, Anonymous trn said...

I was thinking more about the math for the omer question this afternoon, the last day of Pesach.

Earlier, I hadn't really been strict in the math in outlining the limitations for the values of x and y when 3y = 2x, as it didn't seem necessary when those limitations felt obvious and the problem expected to find only one answer and that answer became clear quite quickly.

But of course there are an infinite number of values for x and y where y = 2/3(x). In thinking about the limits, I became puzzled as it seems I found that there are two and not "exactly one day of the omer" that fulfills the requirements of the problem. What am I missing?

Because the values for x and y apply to days, negative numbers are not applicable, as I stated previously. But can they be 0? Both values cannot be 0 because the counting begins with day one.

(Even if the equaltion allowed it, neither value can be 0 because when a value is zero, the nature of the Hebrew is such that the parallel structure would not happen.)

Therefore, the values must not only be non-negative, but must be positive.

Again because days are involved, the values must be integers. Even though (.3,.2) or (1/2,1/3) would be acceptable values for the equation, they do not work for the problem.

Therefore, the values must be positive integers.

How high can the values go? (30,20) or (9,6) could satisfy the equation, but we only count for 49 days, for seven weeks. For the x + 10y half of the equation, corresponding to counting up to 49 days, x can only go as high as 9 because when x (ones column) reaches 10 it is y (tens column) that changes instead, and y only goes up to 4 because once we hit counting in the 50s it is Shavuot. For the 7x + y half of the equation, corresponding to counting up to seven weeks, x goes up to 7 for the full seven weeks, and y goes no higher than 6 because when y (days) hits 7 it is x (weeks) that changes instead.

Therefore, x can only be {1, 2, 3, 4, 5, 6, 7} and y {1, 2, 3, 4}.

Previously, when I found that (3,2) satisfied the equation 3y = 2x, I stopped there. Thinking about the equation better stated as y = 2/3(x) and about the limits I had now figured, I realized that (4,6) could also work.

Is that correct? Do we count day 46 of the omer as day 6-and-40, that is, 6 weeks and 4 days? If so, how is there "one-and-only-one correct answer" to the trivia question?

At 4/21/06, 6:58 AM, Anonymous trn said...

Oops, that's (6,4) not (4,6).

Sorry the above is so long. I should have thought more about the limits in the first place.

Oh! I just looked at the Hebrew. Now I'm thinking that the reason there is only one correct answer is that the sentence for the 23rd day uses esrim (twenty) and shnei (two), and which are perhpas not considered parallel as they aren't related words, making the 23rd day not the answer. Is that right?

I had assumed that the mention of needing knowledge of Hebrew grammar referred to understanding the format of the sentences, the counting, not realizing that it might have to do with noticing the word roots.

If that is the case, then the exactly one correct answer must in fact be: the 6-and-40 (46th) day is 6 weeks and 4 days!

If that is correct, then this is not only a clever trivia question but also a tricky one. In doing the math and knowing there is only one correct answer, it is easy to figure that the answer is the 23rd day and stop there, since that is the solution immediately obvious when the math is done as I had originally done it and when one doesn't think about, as I hadn't, the words for twenty and two, or for ten and one for that matter, not being parallel.

If this is so, then the limits described above are in fact even stricter. Because asarah and asar are not related to echad and esrim is not related to shnei, y can equal neither 1 nor 2. So, y can only be {3, 4}, though the set of possible values for x remain the same. Using these new limits and the equation, the only possible answer is the 46th day.

I don't think I previously realized that the words for ten and twenty share the root ayin-sin-reish and that the word for twenty is not related to the word for two. Shouldn't twenty be esrayim as it is two tens? Why is shnayim two and not twenty as shloshim is thirty and so on?

This was a good exercise. Thank you.

At 4/21/06, 5:31 PM, Blogger Elie said...

TRN: You got it exactly - and saved me the trouble of giving the long winded explanation myself!

As for your last question, I don't know why the Hebrew word for twenty is "esrim" and not "shiniyim" - but as you point out, it's that fact that causes this problem to have one and only one answer.

Hope you all had a wonderful Pesach!


At 4/23/06, 12:13 AM, Anonymous trn said...

Thanks Elie. I'm sure you would have been more concise than I.


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