One must be aware of a common balance{physical balance wherein we place weights on the one pan and object to be weighed on the other pan}.
We have seemingly identical 12 balls of which 11 are exactly equal in weight and one is an "odd ball".We do not know whether the odd one is heavier or lighter than the others.
What is the lowest number of weighing you need to identify the "odd ball"?
Needless to say,the higher the number of weighing,the easier it will be to find a method of locating the odd ball.
Can it be accomplished with just 3 weighing?
This puzzle along with a brilliant answer with just 3 weighing was given by my friend and colleague Rajat Ray who shares my passion for odd and ingenious puzzles.Thank you,Rajat!
I am sure most of you are aware of the game 'chess'and its elementary rules.In case surprisingly any reader is unaware of this game do not despair.
You are requested to keep 8 queens in the chessboard in such a way that no queen is able to kill another queen.(No quarrels in our harem!)Again for the benefit of friends not aware of the rules of the game, a queen can move and hence kill by making basically two types of moves on the chessboard -all four perpendicular directions from whichever square she is placed;all four diagonal directions from whichever square she is placed.Her movement is restricted as far as this problem is concerned only by the four borders-she cannot rebound after reaching any border square.
Now I will break this problem into three portions: Here are two so called
“thought problems” for you. It is said that Albert Einstein was fond of
“thought experiments” and used it as a powerful tool (or rather tried to use, I
should say) against protagonists of the then new “quantum theory”. We are
nowhere near that league but, who knows, which Einstein is hiding among our
viewers? One can use, of course, pen
and paper, to remove any cobwebs in the mind. A man, say, Tom, climbs a
mountain through a fixed route on a weekend- Saturday. He starts at 06.00 hrs
at the bottom of the mountain and climbs with totally haphazard speed (totally
unpredictable varying speeds) and reaches the top of the mountain by
noon-12.00hrs. Having done enough mountaineering for a day, he decides to enjoy
the scenery and take the remaining day off on the peak. The next day, exactly at
06.00hrs sharp, he starts to climb down again using the same path, which he had
taken the previous day; again the speed of climbing down is also totally
haphazard and totally unpredictable. He manages to reach the bottom from where
he started a day earlier exactly at 12.00 hrs noon. Now, given that he climbed both
up and down the mountain at totally erratic speeds but with the time of
commencement and completion being the same, will there be any point of
elevation (or to say in other words, a location in the path) he was present at
the same time on both the days? Obviously there are possible
answers: a) No, can
never be; erratic speeds preclude that. b) May be, one
can never be sure. c) Yes,
definitely. What is the answer you will
vote for? Arthur and David were friends
and David owned a motorboat, which they normally use in the still waters of a
nearby lake. The boat always a steady speed of, say 25-km/ hr in still water. On one vacation, they both decide
to haul this boat to a riverside and do a river cruise from some point A to
point B and return to A. The current of the river was say, 10km/hr. David said
that because the river flowed with a reasonably fast current compared to the
boat speed, it will take a longer time to cover the same total distance in the
river compared to the lake as there is no current in the lake. He said that
they should plan accordingly. Arthur disagreed with him
completely. He maintained that though the river had a current, whatever speed
they lose while going upstream will get compensated when they come back
downstream and after all the distance traveled up and down the stream, whatever
may it be is the same. a) Who is correct? b) Are both partially correct? c) Are both wrong? d) What will the difference in
time, if any, will
depend on? The Great Train conspiracy (Contributed by K. N. Jayakumar) Joe has an aunt Marie living 50 miles to his east and another aunt Clara living 50 miles to the west. Joe lives close to the railway station and decides to visit one of his aunts every week. There are trains to both heading East and West ; the number of trains are equal in both the directions , in fact, equal numbers every hour, Joe decides to adopt a simple system which will also ensure that he does not have to waste time waiting in his station. He will go the station whenever he is free and take whatever train happens to come to the station next and go east bound to visit aunt Marie or west bound to visit aunt Clara. He figures that over a period of one year , this arrangement should work out all right . To his amazement , at the end of the year, aunt Marie is very upset with him for being very mean and partial in his affections; her complaint was that he has been paying much larger number of visits to Clara. Well ,assuming that Clara does not have a beautiful daughter nor she cooks much better than Marie - What do you think has happened here? PUZZLE-9 In the court of "Queer Land" where many queer things happen, one day the king called his sage who was the teacher of his princes. He wanted to check the intelligence of the newly appointed teacher. So he called the sage and gave him the following task. "You are given 4000 oranges and a dozen(12) baskets. The baskets are quite large and let us assume that there will be no problem of capacity and they can hold any number of oranges. You need to distribute all the oranges in these 12 baskets after which the baskets will be sealed. You should have placed the oranges among these 12 baskets in such a way that, no matter what number of oranges is demanded by me subsequently, you should give that many number of oranges in terms of baskets –i.e., you are not allowed to break up any basket. The number of oranges demanded may be 3789 or 121 or 2183 or any such number .You should hand over the oranges demanded in terms of a few or all baskets( in case 4000 is demanded)." The sage, who was a very intelligent man, after a little thought agreed to do it and requested the king to provide him the oranges as well as those extraordinary baskets. Will the sage be able to do it? Can you do it? How will you do it?
PUZZLE 5
A CHESS BOARD HAREM
A chessboard is basically 8 X 8 square board of alternating white and black squares.(You guessed it!-64 squares.)
If not, can you think of an algorithm by which it can be computed in a computer?
AN UPHILL TASK?
ANSWER TO PUZZLE 6
PUZZLE-7
TO BOAT AGAINST THE CURRENT?
ANSWER TO PUZZLE 7
PUZZLE 8
ANSWER TO PUZZLE 9
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