Too Cool To Expand

The number of hens and eggs have direct variation, but the number of hens and days have an indirect variation. Thus, the answer will be three hens.

E4
Trust some people to be nitpicky. A V Ramana Rao at raoavr@gmail.com - he of the test match hat-trick hall of fame problem - has a rather empirical observation regarding why the hole in a metallic doughnut configuration expands on heating. As he argues, this is because it inevitably assumes the material of the doughnut has a positive coefficient of thermal expansion.
But, not to put too fine a point on it, apparently there are materials such as zirconium tungstate and scandium trifluoride - if you please - to mention only two such dastardly deviants, which have a negative coefficient of thermal expansion - meaning they contract when heated. Can you believe it?
However, my question is simple: what happens if such materials are cooled instead? Like, do they keep expanding continuously? (After all, the above mentioned zirconium tungstate is almost world famous for contracting all the way from 0.3 to 1050 Kelvin and would probably have merrily continued to do so, even beyond, if it wasn't for the fact that it begins to degrade by then.) And if so - to maintain my line of thought - what happens if the troublesome tungstate is cooled to as close to absolute zero as possible? Does it begin to exhibit near infinite volume/mass? Cool thought, no? Or do you want to rush into the Google section now to solve the questions before they're written?

DEAR MS

(The question was: "A hen and a half can lay an egg and a half in a day and a half. How many hens are needed to produce 12 eggs in six days?" - MS)
Invariable-Hens-Dept:
Three hens will be needed to lay 12 eggs in six days. Was a nice one to crack while having omelettes on a Friday morning.

• Yakub Lokhandwala,

ylokhandwala@gmail.com
The number of hens and eggs have direct variation, but the number of hens and days have an indirect variation. Thus, the answer will be three hens.

• Sunitha Jaayashankar,

sunithajayashankar@hotmail.com
(Regarding the outcome of the following race between A, B, C, D and E, people have had some surprisingly similar views. - MS)
Racing-Time-Dept:
It is easy to see that D cannot be first; C second and B third. This narrows down the first to B and second D or A. Further elimination will lead to the correct order being BAEDC. This will ensure the predictions 1, 3 and 5 are completely incorrect. Prediction 2 is correct with respect to positions 2 and 3 (AE) and prediction 4 is right on positions 1 and 5 (BC). The key is to recognise that the two correct predictions need not be so in respect of the same positions between them.

• Saikrishna S,

saikrishna.s1998@gmail.com
(And the third problem was: "Why are mountain-tops cold, considering the solar heat per unit area on a mountain is about the same as at sea level?" - MS)
Height-Of-Cooling-Dept:
At high altitudes, atmospheric pressure drops. The relation between temperature and pressure is such that if air pressure increases, the temperature also increases (as in a bicycle pump). Likewise, decreasing the pressure results in a decrease in temperature (as in the case of a spray can). This is what happens at the top of mountains - a decrease in pressure results in a decrease in temperature too.

• Saifuddin S F Khomosi,

saif_sfk@hotmail.com
(Also, air ascending the side of mountains expands and, therefore, cools as it moves into less atmospheric pressure at higher altitudes. - MS)

ENDGAME(S)

1.   You're given a fixed-span compass and asked to draw a circle on a sphere and then on a flat sheet of paper. If the compass is big, the circle on the sphere will be smaller than the one on the paper because its diameter slices through the sphere. But which circle has more area?
2.   Why does it take longer to raise a flag to half-mast than to full mast? 
(To get in touch with Mukul, mail him at mukul.mindsport@gmail.com)

• Mindsport