Tumbling Tumblers

E4
Four glasses are placed in the four corners of a square rotating table, each glass either up or down. You have to turn them all in the same direction, either all up or all down. You may do so by grasping any two glasses and, optionally, turning either over. However, there are two catches: you are blindfolded and the table is spun after each time you touch the glasses. Assuming that a bell rings when you have all the glasses facing the same way, how do you do it?
(I don't want to have to tell you that the glasses are unconed - that is, they are totally parallel walled because even if blindfolded, one can always make out whether a glass is up or down by simply checking the top with a finger. I say this only so that people don't assume blindfolds blindfold all senses.)

DEAR MS
(The problem was regarding the word which had to be generated by clues given by three other words. Only one person got it right with correct reasoning and logic. - MS)

A-Word-In-Hand-Dept:
(1) FOIL: Foil is a type of sheet metal. Foil means thwart. Foil is a sword; (2) TIME: Time Machine is a title. Spacetime is a well-known term. Clock shows time; (3) PRESENT: Gift is a present. The present time is now. To give is to present; (4) BEAUTY: Beauty and the Beast and Black Beauty are both titles. "Beauty is only skin deep" is a  saying; (5) DOUBLE: A mirror shows your double. Doppelganger is your double. Body Double is a movie; (6) MICKEY: Mickey Mouse is a cartoon character. Mickey Mantle is a baseball player. Mickey Finn is a drink; (7) MONOPOLY: Mono indicates one. Monopoly is a game and a term related to business; (8) JAVA: Java relates to computer graphics. Java means coffee. There was a Java Man; (9) LEE: Lee's first name is Bruce. He was known as the Dragon. He created martial arts style - the way of the intercepting fist; (10) MICRO: Bill Gates started Microsoft. Minute and micro are synonyms. There are microbreweries; (11) MAGE: Mage and wizard are synonyms. Mage uses magic. Mage is an anagram of game.
- Saifuddin Khomosi, saif_sfk@hotmail.com

(The second problem was whether five samples could be balanced in a 12-slot centrifuge which had equally spaced slots around a central axis. - MS)

Slot-Of-Samples-Dept:
If there was only one specimen, we would have had to add another "dummy" one and place it diametrically opposite to the original one. In the case of five samples, we again add another dummy sample and place them in slots numbered 12, 2, 4, 6, 8 and 10 or 1, 3, 5, 7, 9 and 11.
- Dhruv Narayan, dhruv510@gmail.com

(The third puzzle was: "How many positive integers are there, in which no digit occurs more than once?" - MS)

We're-Positive-Dept:
One digit: 9 numbers; Two digit: First digit can be any of 1 - 9, second digit can be anything other than the first digit from 0 - 9. Hence can have 9*9 = 81; Three digit: 9*9*8 = 648 numbers; Four digit: 9*9*8*7 = 4536 numbers; Five digit: 9*9*8*7*6 = 27216; Six digit: 9*9*8*7*6*5 = 136080; Seven digit: 9*9*8*7*6*5*4 = 544320; Eight digit: 9*9*8*7*6*5*4*3 = 1632960; Nine digit: 9*9*8*7*6*5*4*3*2 = 3265920; Ten digit, 9*9*8*7*6*5*4*3*2*1 = 3265920. So, the total such numbers we can have are 8877690.
- K Sathyadev, sathya2008k@gmail.com

ENDGAMES
1. An ice cube is floating in a beaker of water, with the entire system at 0 degrees centigrade. Just enough heat is applied to melt the ice cube without raising the temperature of the system. What happens to the water level in the beaker? Does it rise, fall or stay the same?
2. In some countries, one can buy a pear flavoured drink with a real pear inside the bottle. The pear is whole and ripe, and the bottle is genuine; that is, it hasn't been cut in any way. In that case, how did the pear get inside the bottle?
(Mukul can be reached at
mukul.mindsport@gmail.com)

• Mindsport