An old friend of mine had a little daughter named Chini when he was just a new friend of mine. Meaning Chini is now married with a couple of kids and lives in Australia. Anyway to get back to when she was little -- she had once come over to my house with her parents and, as usual, kept asking me weird puzzling question because she knew I was interested in them. “Would a blind man be able to use invisible ink?” she asked. I thought that a was a nice one but trivial. Then she goes, “How will he know when the ink’s has finished?” Even better I thought before she asked the real punch line: “How can even a non-blind person know when his invisible ink has finished?” Got you too, right?
Meanwhile a hydrogen balloon is rising skywards. Its potential energy is increasing and so is its kinetic energy. Something wrong here somewhere?
(The problem was: “Given a circle where seven dots are placed anywhere on its circumference, what would be the maximum number of regions into which it could be divided?”)
A single region may be formed by connecting any two given points on the circumference of a circle and the rest by the intersection of another such segment. For a circle with ‘n’ points on its circumference, we have ‘nC2’ possibilities for a single segment and ‘nC4’ possibilities for a point of intersection with other such segments. The maximum number of regions into which a circle with seven dots placed anywhere on its circumference can be divided =1+7C2 +7C4 = 1 + 21 + 35 = 57. -- Narayana Murty Karri, firstname.lastname@example.org
(The second problem was: “If 0313 = 1, 7662 = 2, 3213 = 0, 1111 = 0, 6666 = 4, 9881 = 5, 6855 = 3, 7756 = 1, 1012 = 1, 5555 = 0 then what does 2581 = ?”)
As very small as well as large numbers correspond to the same number (example: both 7756 and 0313 map to 1) and everything maps to a single digit, it led me to believe the trick is not in subjecting the digits to heavy metamorphosis but in something simple and elegant. I started looking at the shapes of the numbers and interchanging them too. Finally it dawned. Count the number of circles that make up each of the four digits. In 2581, there are two circles in 8 and none in other digits. The answer must be 2. -- Saishankar Swaminathan, email@example.com
(The third one was a rebuff from two readers regarding the level of water falling or rising when an ice cube floating on it melts at 0 degrees C)
Dilip is correct. Ice at 0 degrees has a lower density than water at 0 degrees because the hydrogen bonding gives water a structure with considerable space between the molecules, making it expand in size becoming less dense in a solid state than in a liquid one. He also correctly states that water becomes ice at zero degrees. Exchanging latent heat turns water into ice. Only by the exchange of that much amount of energy can you change the state to solid. -- Shashi Shekher Thakur, firstname.lastname@example.org
As one of the “stupid” readers who attempted to solve the puzzle, treating the liquid at 0 degree Celsius as water and not ice, I would like to point out that liquids can be supercooled and super heated. Meaning, under certain conditions water can be cooled below zero degree Celsius without freezing and heated above 100 degrees Celsius without boiling. So, unless one wants to nitpick, water can stay in liquid state at 0 degree Celsius. -- Balagopalan Nair K, email@example.com
The water level neither rises nor falls; it stays the same. The reason an ice cube floats is because its volume has expanded during crystallisation. –Meenakshi Mehta, firstname.lastname@example.org
BUT GOOGLE THIS NOW
1. A man walked to an automated security gate when a recorded voice uttered “12”. The man replied “6” and was let in. Another man approached the gate and heard “6” to which he replied “3” and was let in, too. Watching this, I went to the gate and heard the voice say “8”. When I replied, “4”, I was not let in. What should I have actually said? – (Submitted by Sheikh Sintha Mathar, email@example.com)
2. UNCERTAINTY is to HEISENBERG as UNDECIDABILITY is to . . . ?
— Sharma is a scriptwriter and former editor of Science Today magazine.(firstname.lastname@example.org)