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Q: There are 7 thieves.. They stole diamonds from diamond merchant & run away in jungle.. While on runin Night sets in & they decide to rest in jungle.. When everybody's asleep two of them who r
closest frnds get up & decide to divide the diamonds among them & run away.. So they start distributing bt they found that one diamond was extra.. So they decide to wake up 3rd one & divide diamonds gin.. Only to their surprise they stil find one diamond extra.. So they decide to wake up fourth.. gin one diamond is spare.. 5th woken up.. Stil one extra!! 6th.. Stil one extra.. Now they wake up 7th one & diamonds are distributed equally.. How many diamonds in total they stole??
A: Those saying 49 haven't read the question carefully - the difficulty is that the remainder each time has to be just 1 - and while you get the right remainder if you divide 49 by 2,3,4, or 6, [ it doesn't work when you divide it by 5. [ 301 is the smallest answer (and 721, 1141, 1561, 1981, and so on adding 420 each time). 2 x 150 +1 3 x 100 + 1 4 x 75 +1 5 x 60 +1 6 x 50 + 1 7 x 43 exactly. What
you need is a number which can be exactly divided by 7, which is one more than a number which can be divided exactly by 2,3,4,5 and 6 (and all of those are going to be multiples of 60 as that is the smallest number divisible by all of them). Go through them and check if divisible by 7 - 61, 121, 181, 241, 301 (yes), 361, 421, 481, 541, 601, 661, 721 (yes), 781, 841, 901, 961, 1021, 1081, 1141 (yes), 1561 (yes) 1981 (yes) - so from there on it is every 420. So, for example 43981 also works - that is 1981 plus 100 x 420: 2 x 21990 +1 3 x 14660 +1 4 x 10995 +1 5 x 8796 + 1 6 x 7330 +1 7 x 6283 exactly. There are actually an infinite number of correct answers - try dividing 3,634,141 diamonds. Uthpala got close to a right answer (with 720) - but forgot to add the essential final diamond to make it exactly divisible by 7. ] ]
khema|Points 20|
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Asked 6/30/2013 6:03:35 AM
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