Sunday, Fun Day (#2)

Sundays I like to post something fun in a puzzle or recreational math line. This starts a little slowly but I do get to some numerological relevance after a build-up, so bear with me if you like that sort of thing ...

The past week saw the United States finally and belatedly coming into compliance with the Jerusalem Embassy Act of 1995, with President Trump’s order to move the American Embassy in Israel to that country’s capital in Jerusalem. 

The aforementioned law, which stipulated that half the State Department’s funding should be forfeited starting in 1999 until they moved our embassy to Israel’s capital, in accordance with usual custom and common sense. In spite of the Act’s passage by wide margins (374-37 in the House, 93-5 in the Senate), the embassy remained unmoved and the State Department saw no inconvenience as a result.

The last of the five Senators who had voted Nay departed the Senate in 2010. That was Robert Byrd, the notorious former Klansman Democrat from West Virginia, who left the Senate upon his death that year, R.I.P.

The date of the Trump announcement is foretold numerologically in the cube root of the year, 2010, when the last Senate opponent to the 1995 bill left office. That cube root is 12.6 2017.

Soon it will be 2018 A.D., but the Hebrew calendar has a different numbering system for the year that started in September. To find it, write 2018. On the next line, copy the 8 below:

2  0  1  8

__ __ __ 8

Then take the digit you just wrote (8) subtract the digit above and to the left, and write that in the next spot. Eight minus one is seven:

2  0  1  8

__ __ 7  8

Continue. Seven minus zero is seven. Seven minus two is five.

2  0  1  8

5  7  7  8

And the Hebrew calendar year is 5778.

This is a triangular number, by the way. (The spirit of Dr. Matrix explained those in this post.) Perhaps President Trump is moved to support Israel’s capital this way because of an affinity with the current Jewish calendar year, since Trump is the 45th President, elected in 2016, and 45 and 2016 are also triangular numbers.

There is a simple test for whether a given number is triangular, which I “discovered”. (It’s not deep mathematics or anything, but I’ve never seen it published.) Take the number, double it, add 0.25, take the square root, and subtract 0.5. If the result is a whole number, the original number was triangular. Applying this to 5778 gives 107, so 5778 is the 107th triangular number: it is 1+2+3+...+105+106+107.

I’ll close with an original seasonal puzzle for the stout-hearted: if you’ve read this far you’re probably a mathie like me. The letters in MERRY CHRISTMAS each stand for a digit, the same letter for the same digit throughout. So MERRY is a five-digit number and CHRISTMAS is a nine-digit number, and the R’s stand for the same digit wherever they appear, as do the S’s and so on. (The word for this kind of puzzle is "cryptarithm".) So here is the puzzle, and it's a tough one: If MERRY is a perfect square and CHRISTMAS is a triangular number, what are the numbers?