# Problematics squares off with Santa

## Join Santa Claus in some arithmetic and on a journey from the North Pole to equator and back.

Santa sends out a mathematical message as he sets off. (Source: free clip art from yopriceville.com)

Just back after three months out of service, Problematics started to pull a fast one on all of us. Can we take another break for just Christmas week, the blog tried to tempt me, but I put my foot down on behalf of all you readers. The final deal was that Problematics would run without exerting itself. In other words, the puzzles this week are borrowed, not my own.

The first one comes straight out of a book, whose cover price was Rs 20 when I bought it as a student. It is one of twin volumes edited and compiled by the late David Pritchard, former editor of the UK’s ‘Games & magazine, though I cannot instantly recall which one of the two had this particular puzzle. It concerns the message from Santa Claus printed in the illustration above.

Santa, as you can see, uses 10 characters from the English alphabetical system — M, E, R, Y, X, A, S, T, O, L. Now each of these stands for a particular digit in the international decimal system. The correct substitution is where you come in.

Puzzle#27A: Replace each letter with the correct digit so that when you finish, you have four perfect squares in place of MERRY, XMAS, TO and ALL. It can be done with reasoning and elimination.

The second puzzle comes from my old friend Arijit Das Gupta, now settled in Kolkata. It’s an absolute gem little known even among puzzle enthusiasts. I ran Arijit’s original version in print in 1993 — not many readers solved it — and have now tailored it to fit the current season while going online.

His sleigh full of gifts, Santa rides out of his home in the North Pole at 7 pm, heading along a single line of longitude towards the equator. He stops countless times along the way, tossing his gifts right and left through the chimneys of the houses of various children. The latitudes of these halts follow no fixed pattern. It’s exactly 7 am (North Pole time) when he reaches the equator, from where he tosses more gifts, long distance, through the chimneys of children living in the southern hemisphere. Then he goes to sleep.

When he sets off on the return journey, he calculates that it is once again 7 pm back home. As he retraces the original line of longitude, he discovers that he is still carrying some gifts, meant for northern children he had forgotten the previous day/night. So he makes amends, stopping at various points and tossing his gifts about, the halts and the homes once again not following any pattern. When he finally reaches home, older, wiser and tireder, Santa notes with amusement that it is exactly 7 am.

Puzzle#27B: Prove that there is one point on the line of longitude — not counting start and finish — where Santa was at exactly the same time on both days.

What you wrote

Given the long break, eight responses to the comeback week’s puzzles is not bad going. For the answer to the Teen Patti puzzle, let’s begin with a look at Sampath Kumar V’s tables, which would qualify as The Gambler’s Essential Guide to Probability Theory.

A few readers got the probabilities wrong, maybe because they were unfamiliar with what qualifies as “cards in sequence”. Card players follow the sequence A-2-3-4-5-6-7-8-9-10-J-Q-K-A. So Q-K-A is a straight or a run, but not K-A-2. Everyone who tried the puzzle, however, rightly pointed out that there is a flaw with Teen Patti.

Hi Kabir — Nice to have you [and your puzzles of course ;)] back !! I think both puzzles were easy this time. The answer to Puzzle#26A will be that Teen Patti has the flaw. The occurrence of Trio will be more than that of Straight Flush. Trio will occur 52 times ( 13 trios and 4 ways to select 3 suites) whereas that for Straight Flush will be 48 (4 ways to select suite and 12 straight combinations). Will await next week’s puzzles.

— Anirudha Hulsurkar (IIT Roorkee)

***

Dear Kabir — For Puzzle#26B, well, it’s the male nightingale that sings. Neither Sarojini Naidu nor Lata Mangeshkar is male.
— Anindita Basu (IBM India, Allahabad)

Solved both puzzles: Sanjay Gupta (New Delhi), Biren Parmar (Texas A&M University), Jaysun Antony Alumkal (IIM Raipur), Sreenvas Subramanyam (IIM Raipur), Sampath Kumar V (IIM Kozhikode alumnus), Anirudha Hulsurkar (IIT Roorkee)

Solved first puzzle: Rajat Gupta (IIT Roorkee alumnus)

Solved second puzzle: Anindita Basu (IBM India, Allahabad)