The following fourteen people live on the same block:
The girls:
• Alice, Ann, Caroline, Louise, Mary, Martha, Rose.
The boys:
• Andrew, Charles, David, John, Paul, Peter, Richard.
There are seven houses on each side of the street. Each person lives alone in one of them. If the following additional information is also known:
- Mary lives next to a girl.
- John lives diagonally across from two boys.
- Richard lives next to Charles.
- Ann and Martha live on different sides of the street.
- Caroline lives between two boys.
- There are more boys than girls on the side where David lives.
- Rose lives across from Ann.
- Alice lives on a corner.
- Charles lives mid-block.
- Andrew lives across from Alice.
- Paul lives across from Mary.
- Martha lives diagonally across from Caroline.
- Richard lives across from Martha.
- Louise lives as close to Rose, as Charles to Andrew.
- Mary and Caroline live on the same side of the street.
- Ann lives on a corner.
Who lives across from Peter?
Taking these four clued first, as they define who lives at the two ends of the street. This reduces the set that has to be permuted to 10 from 14. I should have also done Charles at the middle of the block, but I didn't think that far ahead.
Ann lives on a corner.
Rose lives across from Ann.
Alice lives on a corner.
Andrew lives across from Alice.
and the remaining clues:
Mary lives next to a girl. +
John lives diagonally across from two boys. +
Richard lives next to Charles. +
Ann and Martha live on different sides of the street. +
Caroline lives between two boys. +
There are more boys than girls on the side where David lives. +
Charles lives mid-block. +
Paul lives across from Mary. +
Martha lives diagonally across from Caroline. +
Richard lives across from Martha. +
Louise lives as close to Rose, as Charles to Andrew.
Mary and Caroline live on the same side of the street. +
The clue concerning Louise was not included in the code, so that left some manual comparison among several street layouts.
%Assume Ann on NW, Rose on SW
% Alice and Andrew at East end
girls=["Alice" "Ann" "Caroline" "Louise" "Mary" "Martha" "Rose"];
boys=["Andrew" "Charles" "David" "John" "Paul" "Peter" "Richard"];
inner=setdiff([girls boys],["Ann" "Rose" "Alice" "Andrew"]);
layouts=perms(inner);
endsets=["Ann","Alice","Rose","Andrew";"Ann","Andrew","Rose","Alice" ];
sz=[7,2];
for i=1:length(layouts)
for ends=1:2
layout=[endsets(ends,1) layouts(i,1:5) endsets(ends,2); ...
endsets(ends,3) layouts(i,6:10) endsets(ends,4)];
layout=layout';
mary=find(layout=="Mary");
if ismember(layout(mary-1),girls) || ismember(layout(mary+1),girls)
john=find(layout=="John");
[row,col]=ind2sub(sz,john);
if ismember(layout(row-1,3-col),boys) && ...
ismember(layout(row+1,3-col),boys)
richard=find(layout=="Richard");
charles=find(layout=="Charles");
if abs(richard-charles)==1
if charles==4 || charles==11
paul=find(layout=="Paul");
mary=find(layout=="Mary");
if abs(paul-mary)==7
% ann=find(layout=="Ann");
martha=find(layout=="Martha");
if martha>7
caroline=find(layout=="Caroline");
if ismember(layout(caroline-1),boys) && ...
ismember(layout(caroline+1),boys)
if abs(martha-caroline)==6 || ...
abs(martha-caroline)==8
if abs(richard-martha) ==7
[~,c1]=ind2sub(sz,mary);
[~,c2]=ind2sub(sz,caroline);
if c1==c2
david=find(layout=="David");
[~,side]=ind2sub(sz,david);
boycount=sum(ismember(layout(:,side),boys));
if boycount>3
disp(layout)
disp(' ')
end
end
end
end
end
end
end
end
end
end
end
end
end
does not implement
Louise lives as close to Rose, as Charles to Andrew,
as that might be ambiguous depending on the width of the street,
and it finds the following eight layouts of the street:
"Ann" "Rose"
"Mary" "Paul"
"Louise" "Peter"
"Charles" "David"
"Richard" "Martha"
"Caroline" "John"
"Andrew" "Alice"
"Ann" "Rose"
"Mary" "Paul"
"Louise" "David"
"Charles" "Peter"
"Richard" "Martha"
"Caroline" "John"
"Andrew" "Alice"
"Ann" "Rose"
"Mary" "Paul"
"David" "Peter"
"Charles" "Louise"
"Richard" "Martha"
"Caroline" "John"
"Andrew" "Alice"
"Ann" "Rose"
"Mary" "Paul"
"David" "Peter"
"Charles" "John"
"Richard" "Martha"
"Caroline" "Louise"
"Andrew" "Alice"
"Ann" "Rose"
"Mary" "Paul"
"David" "Louise"
"Charles" "Peter"
"Richard" "Martha"
"Caroline" "John"
"Andrew" "Alice"
"Ann" "Rose"
"Mary" "Paul"
"David" "Louise"
"Charles" "John"
"Richard" "Martha"
"Caroline" "Peter"
"Andrew" "Alice"
"Ann" "Rose"
"Louise" "Peter"
"Mary" "Paul"
"Charles" "David"
"Richard" "Martha"
"Caroline" "John"
"Andrew" "Alice"
"Ann" "Rose"
"Louise" "David"
"Mary" "Paul"
"Charles" "Peter"
"Richard" "Martha"
"Caroline" "John"
"Andrew" "Alice"
Only in the third layout above does Louise and Rose's distance apart unambiguously match the distance of Charles from Andrew (3 houses away on the same side of the street):
"Ann" "Rose"
"Mary" "Paul"
"David" "Peter"
"Charles" "Louise"
"Richard" "Martha"
"Caroline" "John"
"Andrew" "Alice"
and it's David who lives across from Peter.
|
|
Posted by Charlie
on 2023-10-06 09:24:24 |
computer-aided solution
