7 thieves steal some Diamonds. 2 of the thieves swindle with others and divide the diamonds between each other in 2 equal parts but one Diamond remains left. Then they call one more thief in their swindle and again divide the diamonds in three equal parts but still 1 Diamond remains left.They call every thief one by one and divide those Diamonds but in every situation 1 Diamond remains left but when they call the 7th and the last thief and divide the Diamonds in 7 equal parts then all diamonds allocated equally. Not a single Diamond remains left. Then find the number of Diamonds. Give a proper solution.
Answers
Answer:
number of diamonds= 7
Answer:
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Step-by-step explanation:
Lets say there are x diamonds, now these diamonds are exactly divisible by 7.
and
x = 1 + R1*2;
x = 1 + R2*3;
x = 1 + R3*4;
x = 1 + R4*5;
x = 1 + R5*6;
x = R6*7;
where R1, R2, R3, R4 and R5 are integers.
From above we can also say
R1*2 = R2*3 = R3*4= R4*5 = R5*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