perplexus.info :: Numbers : Handshakes #2

Handshakes #2 (Posted on 2024-06-08)

Refer to Handshakes, in which:

The Smiths, the Andrings and the Cliffords all hold a big party. Everyone shakes hands with every member of the other two families (no one shakes hands with members of their own family), 142 handshakes in all.

Assuming that there at least as many Andrings as Smiths, and at least as many Cliffords as Andrings, determine:

A) Is there any number larger than 142 handshakes that still leads to a unique solution?

(B) What is the largest number of handshakes if we are told that there is a different number of people in each family?

(D) What is the maximum if there are 4 families, each with at least 2 members, and each with a different number of members?

No Solution Yet Submitted by K Sengupta

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computer findings

| Comment 1 of 4

The code after finding the numbers with unique solutions (within limit of 300 people altogether

goodset=[142 163 177 193];

for goal= 142:300

ct=0;

for tot=5:50

for s = 1: tot/3

for a = s : (tot-s)/2

c = tot - a - s;

if c > 0

if a * s + s * c + a * c == goal

ct=ct+1;

if ismember(goal,goodset)

disp([s a c goal])

end

if ct==1

% disp(goal)

end

Smiths Anddrings Cliffords    handshakes

     1    10        12           142
     1     3        40           163
     3     3        28           177
     4     7        15           193

Posted by Charlie on 2024-06-08 21:57:54

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