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Body Language

27 April, 2006

Guess what I discovered I could do? I found I can list the complete human body in terms of almost all outer parts from the cranium to the Kanyakumari using popular phrases, sayings, saws, some proverbs and several adages and axioms. For instance have a look at Mr Below if you don't believe.

Bad HAIR day; banging your HEAD against a brick wall; BRAIN drain; by the sweat of his BROW; as far as the EYE can see; cut off your NOSE to spite your face; cauliflower EARS; CHEEK by jowl; born with a silver spoon in his MOUTH; button your LIP; bite your TONGUE; armed to the TEETH; by the hairs on my chinny CHIN chin; cut THROAT competition; an albatross around his NECK; a chip on the SHOULDER; casing the JOINT; business at HAND; bend your ELBOW; brothers in ARMS; cross my PALM with silver; bleeding HEART liberal; BOSOM buddies; an army marches on its STOMACH ; back to BACK; contemplate one's NAVEL; as tight as a duck's ARSE; catching him by the BALLS; cool and HIP; break a LEG; between the THIGHS; bee's KNEES; cramp in the CALF; ANKLE deep; bound hand and FOOT; bells on her TOES; cash on the NAIL.

Did I hear you say "So? Big freaking deal"? Then get this: I used only the first three letters of the alphabets beginning each phrase, so that you can quickly stop reading this sentence in mid gasp and check back on the para that just whizzed past your skull. Every one of those aphorisms or epigrams or whatever the hell they're called starts with an A, B or C. No D to Zee, see? So here's the real deal now: Think you can do the same with any other arbitrary three letters – preferably successive ones if possible like DEF, GHI, MNO, STU, etc? If not, admit defeat and we'll both pretend like today never happened in the calendar.

DEAR MS,

Eeking-Out-A-Living-Dept:

The author of the letter claiming the mouse Endgame was wrong forgot the fact that every bottle had a unique selection of mice, a unique binary code as one solution suggested, and that after one month when the mice died the poisoned bottle could be found by simply checking which bottle it was that had been fed to those particular mice.
Anubhav Yadu, a_yadu@yahoo.com

Coming-Of-Age-Dept:

(The Endgame was: "How many numbers between 1 and 1000000 have the sum of their digits as18?" – MS)

The number is 25927. The following formula gives the answer: (18 + 6 - 1)C(6 - 1) - 6*(8 + 6 - 1)C(6 - 1) = 23C5 - 6*13C5. This is easily arrived at once we rephrase the problem as follows: given 18 identical objects, in how many ways can we pack them into six ordered boxes, with the restriction that no more than nine objects are allowed in each box. Without going into details (which would be a mini-puzzle for some readers if you run this solution!), the 23C5 is the number of ways this can be done without the upper limit of 9, and the 6*13C5 is the number of combinations that fail this condition.
Manoj Nair, mnair77@gmail.com

There are 1 + 54 + 615 + 4170 + 21087 = 25927 numbers between 1 and 1000000 whose digits add up to the sum of 18. It was simple and all I had to do was execute a program but thereafter I was more interested in finding out how to do it manually. Happily, all it needed was a knowledge of simple combinatorics. In fact it can be done in minutes with the help of a PC.
Altaf Ahmed, Dubai , UAE

Let us take an example of a four-digit number having digits a, b, c, d. Then the condition is a + b + c + d = 18 where only a can't take 0 as its value. Hence the required number of solutions will be the coefficient of x^18 in (x + x^2 + x^3 . . . + x^9)(1 + x + x^2 + x^3 . . . + x^9)^3. With the help of binomial theorem, we will get the coefficient as 11C3 + 20C3 - (3C1*10C3) where nCr is n!/r!(n - r)!. Similarly we can do for two-, three-, five-, six-digit numbers. The total number of numbers between 1 and 1000000 is (in order of increasing digit numbers =1 + 54 + 615 + 4170 + 21087 = 25927.
Viren Timble, viren_t2005@yahoo.co.in

There should be no early bird criteria for printing names since someone who sends his answer first might have solved it later compared to another guy who solved the puzzle, but may not be in a position to send the answer. (Actually I wait about three weeks so that early birds can be chosen from different categories besides TOI, like website, blogs, overseas print editions, etc – MS)
Hardeep Singh, hs2412@gmail.com

ENDGAME

(Continued from Dear MS,) Along with the answer I found a peculiar series being formed if you find the number of such numbers (digit sum) between 1 and 100, 200, 300, 400, . . . 1000, 1100, 1200, 1300, . . . 2000, 2100, 2200, 2300 . . . . They are 1, 3, 6, 10, . . . 55, 57, 60, d, . . . 118, 121, 125, 130. Can any mathemagician with some logical sequencing skills find out what kind of series it is and how to calculate the nth number in this series?
Lt Col Sanjay Mohan, Bangalore, India

Posted by geminimay_no 11:56 | Fun Stuff - For All Ages | Comment(4) | Permalink

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