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Seven thieves and diamonds

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There are seven thieves, They steal diamonds from a diamond merchant and run away in jungle. While running, night sets in and they decide to rest in the jungle When everybody’s sleeping, two of the best friends get up and decide to distribute the diamonds among themselves and run away. So they start distributing but find that one diamond was extra. So they decide to wake up 3rd one and divide the diamonds again …..only to their surprise they still find one diamond extra. So they decide to wake up fourth one. Again one diamond is spare. 5th woken up……still one extra. 6th still one extra. Now they wake up 7th and diamonds are distributed equally.

How many minimum diamonds they steal?

Check your answer:-

Tried enough already?
See Solution
Lets say there are x diamonds, now these diamonds are exactly divisible by 7.
and
x = 1 + N1*2;
x = 1 + N2*3;
x = 1 + N3*4;
x = 1 + N4*5;
x = 1 + N5*6;
x = N6*7;
where N1, N2, N3, N4 and N5 are integers.
From above we can also say
N1*2 = N2*3 = N3*4= N4*5 = N5*6 = y

Now y should be divisible by 2, 3, 4, 5 and 6, its nothing but common multiple of all.

LCM of 2, 3, 2*2, 5, 2*3 => 2*3*2*5 => 60

at the same time common multiple + 1 should be divisible by 7 as well.

60 + 1 is not divisible by 7
120(60*2) + 1 is not divisible by 7
180(60*3) + 1 is not divisible by 7
240(60*4) + 1 is not divisible by 7
300(60*5) + 1 is divisible by 7

Thus they must have stolen minimum 301 diamonds.

A man and two gates

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One day a man woke up from sleep to find that he was at an unknown place away from his home.He walked certain distance to reach a bifurcation.Two roads bifurcated at that point one would lead him to his home and the other would lead him to certain death…now his dilemma was this…two man stood at each road.one would always speak truth, the other always lie.They informed him that he could ask just one question to any of them but did not tell him who was who.So,what question he would had asked to reach home safe ?

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Product of 5 different temperatures

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Number Puzzle #66
The product of 5 different temperatures is 12. If all of them are integers then find all the temperatures.


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product of 5 different integers is 12.

Lets consider first product of first 3 smallest integers
1*2*3 = 6
Now if we take the next smallest intege i.e. 4 then the product will become 24 thus we need to go back and consider negative numbers

thus (-2)*(-1)*1*2*3 = 12.

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