1) 'A' and 'B' are positive zeroless 2-digit integers which have one digit in common.
A 6-digit sequence, S, composed of only 3 unique digits, occurs in both A^B and B^A.
Find A, B, and S.
2) 'C' and 'D' are two other positive zeroless 2-digit integers which also have one digit in common.
A 6-digit sequence, T, composed of 6 unique digits, occurs in both C^D and D^C.
Find C, D, and T.
Neither S nor T has any leading zero.
I didn't change the variable names for the second part, but that doesn't affect the answer, given the Bard's quote.
clearvars,clc
for a=11:99
as=char(string(a));
for b=11:99
bs=char(string(b));
abs=[as bs];
if isequal(strfind(abs,'0'),[] ) ...
&& length(intersect(as,bs))==1 ...
&& a~=b
if length(intersect(as,bs))==1
ab=char(sym(a)^b);
ba=char(sym(b)^a);
for i=1:length(ba)-5
if length(unique(ba(i:i+5)))==3
s=ba(i:i+5);
p=strfind(ab,ba(i:i+5));
if ~isequal(p,[])
disp([as ' ' bs ' ' s ' ' ab ' ' ba])
end
end
end
end
end
end
end
disp(' ')
clearvars
for a=11:99
as=char(string(a));
for b=11:99
bs=char(string(b));
abs=[as bs];
if isequal(strfind(abs,'0'),[] ) ...
&& length(intersect(as,bs))==1 ...
&& a~=b
if length(intersect(as,bs))==1
ab=char(sym(a)^b);
ba=char(sym(b)^a);
for i=1:length(ba)-5
if length(unique(ba(i:i+5)))==6
s=ba(i:i+5);
p=strfind(ab,ba(i:i+5));
if ~isequal(p,[])
disp([as ' ' bs ' ' s ' ' ab ' ' ba])
end
end
end
end
end
end
end
finds
1)
A B S The results of the exponentiations
79 94 335375
238202645946674671901844030131688261840455609040130839498451613353756747499045969428775114432599223
68471508951254043301841598310810959122639093018750573711401473264757112263998881
753529803906603364328062684879905074416038191684436076994112942137793353750693678788439419755385754
714791974652553974362629067333843924654151549669661999104
94 79 335375
753529803906603364328062684879905074416038191684436076994112942137793353750693678788439419755385754
714791974652553974362629067333843924654151549669661999104
238202645946674671901844030131688261840455609040130839498451613353756747499045969428775114432599223
68471508951254043301841598310810959122639093018750573711401473264757112263998881
2)
C D T The results of the exponentiations
59 89 432061
403486525674138721277358818163343412346056820000557049137740680894095772750769877883643206109427169
31267361565319605418282649582007448319855547952616453971739
103278611857003616688625589179443206140188442838630835763439139309446407559324649401479846415941859
20164994365747209
89 59 432061
103278611857003616688625589179443206140188442838630835763439139309446407559324649401479846415941859
20164994365747209
403486525674138721277358818163343412346056820000557049137740680894095772750769877883643206109427169
31267361565319605418282649582007448319855547952616453971739
Edited on June 1, 2023, 3:20 pm
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Posted by Charlie
on 2023-06-01 14:51:22 |
computer solution
