### By Mukul Sharma

Published: Fri 28 Oct 2016, 12:00 AM

Last updated: Fri 28 Oct 2016, 2:00 AM

E4
Remember the "is to, as to" problems as in: Blue is to Sky as Green is to Grass, or Man is to Woman as Andro is to Gyno?  Try these 12 on for size now: (1) Strip is to Mobiüs as Bottle is to.? (2) Thought is to Action as Obsessive is to.? (3) Mice is to Men as Cabbages is to.? (4) Sword is to Damocles as Bed is to.? (5) Jekyll is to Hyde as Eloi is to.? (6) 4 is to Hand as 9 is to.? (7) Hollow Victory is to Pyrrhic as Hollow Village is to.? (8) Easy Job is to Sinecure as Guiding Light is to.? (9) Leg is to Ambulate as Arm is to.? (10) Astronomy and Physics is to Astrophysics as History and Statistics is to.? (11) Language Games is to Ludwig as Piano Concerto for the Left Hand is to.? (12) Set of Sets Not Member of Themselves is to Russell as Darkness of the Night Sky in an Infinite Universe is to.?
If you get only two correct, run yourself down yourself. If you get eight to ten correct, you'll be run. If you get all 12 correct, I'll run to the editor and tell him/her to let you run this column for the rest of your life or an eternity - whichever comes earlier.

DEAR MS
(The lone and last lingering problem was the one where you were given 10 statements beginning with "Exactly one statement on this list is false" to "Exactly ten statements on this list is false" and told to choose the only one of them which was true. - MS)

False-And-Truesies-Dept:
Unless I have missed something very profound, if only one statement out of ten is true, then nine must be false: meaning (9) is correct. What is "not easy" about this?
- Hasrat Parkar, hbp1959@gmail.com

The answer is #9. This is because if #10 is true, it will be a contradiction, as there will only be nine false statements. If #8 is true, then there will be nine false statements, another contradiction. So is the case for #7 to #1. But, in the case of #9, nine statements are false and one is true.

When we know that exactly one statement is true, it means the other nine statements are false. This is precisely what the 9th statement implies. So the 9th one holds true.
- Saifuddin S F Khomosi, saif_sfk@hotmail.com

(The other one was about a ten all-digit number exactly divisible by 10. On removing the units digit, the remaining number is exactly divisible by 9. Again, on removing the units digit, the remaining number is exactly divisible by 8. And so on till all the numbers have been knocked off one by one. What's the number? - MS)

Digital-Solutions-Dept:
The number is 3816547290. The units digit should obviously be 0. The fifth place from the left is occupied by 5. All the even places must be filled with even numbers; also, the sum of the first three numbers as well and the first six has to be a multiple of 3. Thus, after trying out many permutations, we arrive at the required number.

(The third problem was: "Although the Celsius and centigrade scales are the same today, originally there were two differences between them." - MS)

Degrees-Of-Difference-Dept:
Anders Celsius devised a temperature scale in 1741, with the boiling point of water as 0° and the freezing point of water as 100°. After his death, this scale was turned upside down, and the scale was given the name centigrade. The other difference is the numerical difference between their zero values, 273.15 K for the centigrade scale and 273.16 for the Celsius scale, a difference of 0.01°.
- Balagopalan Nair K, balagopalannair@gmail.com (Yes, Abirami Sundari, abirami262002@gmail.com, you also got part of it right. - MS)

ENDGAME(S)
1. If I were to tell you that I'd bet you a buck that if you gave me two bucks, I'd give you three bucks in return, would it be a good bet for you to accept?
2. If a year consists of 365 days, then how many times does the Earth rotate during this year? The answer is 366. But the question is why?

(Mukul can be reached at mukul.mindsport@gmail.com)

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