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805+ (Hard)|   Combinations|      
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Bunuel
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At a twins and triplets convention, there were 9 sets of twins and 6 31 Mar 2019, 21:48
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B
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46% (02:48) correct 54% (03:28) wrong based on 103 sessions

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At a twins and triplets convention, there were 9 sets of twins and 6 sets of triplets, all from different families. Each twin shook hands with all the twins except his/her siblings and with half the triplets. Each triplet shook hands with all the triplets except his/her siblings and with half the twins. How many handshakes took place?

A. 324
B. 441
C. 630
D. 648
E. 882
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B
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At a twins and triplets convention, there were 9 sets of twins and 6 01 Apr 2019, 10:36
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Bunuel
At a twins and triplets convention, there were 9 sets of twins and 6 sets of triplets, all from different families. Each twin shook hands with all the twins except his/her siblings and with half the triplets. Each triplet shook hands with all the triplets except his/her siblings and with half the twins. How many handshakes took place?

A. 324
B. 441
C. 630
D. 648
E. 882
Show more

each twin shakes hands 16 times with others not with each other and with 9 triplets; total 16+ 9 = 25
each of triplet shakes hands with 15 triplets and 9 twins ; 24 people
Dividing by two to accommodate the fact that each handshake was counted twice, we get a total
1/2 * 18 * (25+24) ; 9 * 49 ; 441
IMO B
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At a twins and triplets convention, there were 9 sets of twins and 6 28 Apr 2019, 01:31
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Bunuel
At a twins and triplets convention, there were 9 sets of twins and 6 sets of triplets, all from different families. Each twin shook hands with all the twins except his/her siblings and with half the triplets. Each triplet shook hands with all the triplets except his/her siblings and with half the twins. How many handshakes took place?

A. 324
B. 441
C. 630
D. 648
E. 882

each twin shakes hands 16 times with others not with each other and with 9 triplets; total 16+ 9 = 25
each of triplet shakes hands with 15 triplets and 9 twins ; 24 people
Dividing by two to accommodate the fact that each handshake was counted twice, we get a total
1/2 * 18 * (25+24) ; 9 * 49 ; 441
IMO B
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How to make sure that every handshake was counted twice..........From calculated intuition i arrived at the correct answer but not being able to make sure
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At a twins and triplets convention, there were 9 sets of twins and 6 29 Jun 2023, 04:50
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Hi I have a doubt here.
The first Twin shook hands with 16 other twins(lets leave the triplet right now). and that way we are counting 18*16.
Now when the last Twin (i.e.-16) will shook the hand then she will shook with only 15 twin as she has already shook the hands with the first twin in the beginning.

Can you plz clear my doubt.
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At a twins and triplets convention, there were 9 sets of twins and 6 29 Jun 2023, 15:47
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Bunuel
At a twins and triplets convention, there were 9 sets of twins and 6 sets of triplets, all from different families. Each twin shook hands with all the twins except his/her siblings and with half the triplets. Each triplet shook hands with all the triplets except his/her siblings and with half the twins. How many handshakes took place?

A. 324
B. 441
C. 630
D. 648
E. 882
Show more

Each of the 9 × 2 = 18 members of the twins group shook hands with 16 members of the twins group [the total number of twins – himself – his sibling], so this represents a total of

18 × 16 / 2 = 144 handshakes [We have to divide by 2 because person A’s handshake with person B is the same handshake as person’s B handshake with person A.]

Furthermore, each of the 18 members of the twins group shook hands with 6 × 3 / 2 = 9 members of the triplets group. [Of course, this number also accounts for all the handshakes the members of the triplets group made with the members of the twins group.] So, this is a total of 18 × 9 = 162 handshakes.

Finally, each of the 6 × 3 = 18 members of the triplets group shook hands with 15 members of the triplets group [the total number of triplets – himself – his two siblings], so this represents a total of

18 × 15 / 2 = 135 handshakes [Again, we have to divide by 2 because person A’s handshake with person B is the same handshake as person’s B handshake with person A.]

Therefore, the total number of handshakes is:

144 + 162 + 135 = 441

Answer: B
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At a twins and triplets convention, there were 9 sets of twins and 6 09 Mar 2026, 03:31
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