this was asked in IIT entrance exam,, can u solve this question?if yes u can go into IIT easily,,?

Question

well,,
IIT - indian institute of technology,,(world's 3rd best university) had this problem in its entrance exam-->

u have 10 same looking bags,
100 coins in each,,
9 of them has coins weighing 10 gms each,,remaining one has coins weighing 9 gms each,,
u have a digital weighing machine,,with one balance on it,,
only one chance to measure the weight on it,,and find which bag is it that contains the coins weighing 9 gms,,

just give me a method to know which could be the bag,,
^_~

Answer 1

Take one coin from the first bag, two from the second, three from the third, etc. You'll have 1+2+...+10 = 55 coins.

Weigh these 55 coins. The weight will be 10*55 - N grams, for some N. That N tells you which bag had the lighter coins. If the total weight were 547, then you'd know that the 3rd bag had the lighter coins, for example.

Answer 2

That is an old logic riddle. The trick is you put one coin from the first bag, two coins from the second bag, up to ten from the last bag. Then you do one weighing of the pile. If it is short by one gm then bag one had the coins that were 1 gm light, short by two means second bag, and so on.

And what does this have to do with IIT? Do they train you for occupations where your pay arrives in bags?

Answer 3

You take 1 coin from the first bag
................2 coins..............second bag
................3 coins..............third bag
................4 coins..............fourth bag
................5 coins..............fifth bag
................6 coins..............sixth bag
................7 coins..............seventh bag
................8 coins..............eight bag
................9 coins..............ninth bag
...............10coins..............tenth bag

Take one measure with all the coins.
the result will be

(1+2+3+4+...+10)*weight + k
where k is number of 9gms coins picket from the easier bag
So if k=1 then the first bag is the one with 9gms coins in it
if k=2 then the second bag ...........
if k=3 then the third bag .............

...................

Ok so I'm in one of the top IIT university. So what?

Answer 4

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