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Permutations and Remainders (Posted on 2024-05-17)

Determine all the numbers formed by three different and non-zero digits, such that the six numbers obtained by permuting these digits leaves the same remainder after the division by 4.

No Solution Yet Submitted by Danish Ahmed Khan

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computer solution

| Comment 2 of 4 |

nset=combinator(9,3,'c');

for i=1:length(nset)

nsubset=nset(i,:);

idx=combinator(3,3,'p');

nsubset=num2str(nsubset(idx));

for j=1:size(nsubset,1)

v(j,:)=erase(nsubset(j,:),' ');

v2(j)=str2double(v(j,:));

r(j)=mod(str2double(v(j,:)),4);

end

if length(unique(r))==1

disp(v2)

disp(mod(v2,4))

end

finds

>> permutationsAndRemainders
   951   915   591   519   159   195
     3     3     3     3     3     3
>>

Posted by Charlie on 2024-05-17 13:10:26

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