The letters denote a different base ten digit from 0 to 9. No number can contain any leading zero.
It is known that both the relationships are simultaneously satisfied:
1) (AAAU)2= ALUMINE
2) (A+A+A+U)2= A+L+U+M+I+N+E
What is the number denoted by ALUMINE?
It was not necessary to test relationship 2), as relationship 1) implies relationship 2). (i.e., only one number satisfies relationship 1).
clearvars,clc
digs='0123456789';
idx=combinator(10,7,'p');
poss=digs(idx);
for i=1:length(poss)
ns=poss(i,:);
n=str2double(ns);
a=ns(1);u=ns(3);
if ns(1)~='0'
aaau=str2double([a a a u]);
if aaau^2 == n
disp(n)
disp([sod(aaau)^2 sod(n)])
end
end
end
finds
1238769
36 36
where the first line is the value of ALUMINE.
The second line verifies that when condition 1) is met, it follows that condition 2) also is true: the square of the sum of the digits of AAAU equals the sum of the digits of ALUMINE.
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Posted by Charlie
on 2023-09-30 08:28:34 |
computer solution
