The message “MERRY XMAS TO ALL” was sent in coded form by a math prof to all his friends by replacing all the letters with digits. He also noticed that it contained precisely 10 different letters so that he could represent each by a different digit. But then math profs are such squares that he also decided on a code such that each of the words was represented by a perfect square. What was the message? I’m giving an easy one so your much bruised ego can get up and running again from one solution to another. Because there are two answers.
THROUGHPUT
(The problem was about putting something like 150 different kinds of tablets into a jar and them drawing out five of each kind every day for a month. And blah blah. However, the problem was spectacularly misunderstood by most responders as witness below.)
The answer to the Drug Underdose problem is as follows: On the first day of the month you need not put all the 150 (5*30) tablets in the bottle. You put only 29 of each tablet (totally 145) into the bottle, withholding one each of the five different tablets. Then there is no necessity to draw even once from the bottle. -- Dr P Gnanaseharan, gnanam.chithrabanu@gmail.com
(So, just for the heck of it the solution actually is 228091951/ 20821801which is about 10.9544 something. Now see if you can figure out why.)
(The second one was: “Little Gina has a set of four alphabet blocks, with a letter on each side. V and Z are missing. Arranging the blocks in various ways she can spell CHIP, FLUX, FUNK, IRAQ, JOBS, JUMP, QUIT, SKEW, SMOG, SWAB, TUCK and WILD. How are the letters arranged on the blocks.”)
Of course, one may do frequency analysis, use methodical logic and then assign letters to blocks and arrive at the answer which is: ADEHOU, BIKMXY, LNPRST, CFGJQG. But I found an easier way by recalling that this puzzle was first published in some other forum as Baby Tina’s Blocks way back in March, 2003 and obtained the answer from there. Yah, yah, I cheat so what? -- Ajith Athle, ajitathle@gmail.com
Actually three letters V, Z AND Y do not appear in the 12 words given. Thus the four alphabet blocks of Gina together contain 23 letters of the alphabet, which results in one side of one of the four blocks being left blank. The six letters on the six sides of the first block are ADEHOU. The second block contains the letters LNPRST. The third block contains the letters CFGJQW. The fourth block contains the letters BIKMX (only five letters) with one side left blank. -- K Narayana Murty, k_n_murty@yahoo.com
I like your clue of Y by mentioning V and Z. Surely, Gina the Genius will become a great Scrabble player. My methodology involved (1) how many times each letter appears (2) six letters of each block put together (except Y) must appear 12 times, so letters in each of the groups US, UI, USW, USK, UIW, USI, SIW have to be in different blocks; (3) first take up words with common groups of two letters like SW, SO, SB, FU, QI. My starting word was SWAB. -- Abhay Prakash, abhayprakash@hotmail.com
(The third problem was: “The equations below are written in code such that each digit represents some other digit. Break the code, given that each of the following is true in base 10. 8 + 7 = 62; 5 + 3 = 5; 12 + 8 = 23; 50 + 9 = 54; 11*1 = 55; 0 - 9 = 1.”)
The Code: 0 stands for 5, 1 for 3, 2 for 4, 3 for 0, 4 for 7, 5 for 9, 6 for 1, 7 for 8, 8 for 6 and 9 for 2. The given information leads to 3 stands for 0, 6 stands for 1 and either 1 for 2 or 3 and 5 for 6 or 9. Considering all the information provided gives the rest of the answer. Quite an enjoyable workout. -- J Vaseekhar Manuel, orcontactme@gmail.com
Using conditions like 3 is 0 (since 5 + 3 = 5), and 1 has to be either 2 or 3 (22*2 = 44 and 33*3 =99), one should be able to solve the problem. Which is: etc etc etc. -- Ravi Nidugondi, ravi.nidugondi@gmail.com
BUT GOOGLE THIS NOW
1. You must have noticed that sometimes some clothes like thick cottons acquire a shininess when they’re ironed. What is this due to?
2. Sorry, but aeroplanes don’t fly because of the Bernoulli principle. (Otherwise how would they fly inverted?) So what keeps them airborne then? Have fun on Google.
Sharma is a scriptwriter and former editor of Science Today magazine.(mukul.mindsport@gmail.com)