In an alphametic, each letter is represented by a different base ten digit from 0 to 9 inclusively. No number can contain any leading zero.
Solve this alphametic, knowing that:
SEIS is a triangular number, and:
SIETE is a prime number, and:
DIEZ is a triangular number.
*** In Spanish, the first ten counting numbers are: uno, dos, tres, cuatro,cinco,seis,
siete, ocho, nueve and diez.
*** Adapted from a puzzle appearing in Missouri State University Problem Corner.
To start, we want a list of 4-digit triangular numbers whose first and last digits are the same and whose middle two digits do not match, for SEIS. The maximum limit of the nth triangular number is found by taking the triangular root (variable tr, below, -- analagous to square root) of 9999. The non-matching of the middle two digits is assured by checking that exactly 3 unique digits are used.
For each such triangular number we also want those other triangular number with the same middle two digits but in reverse order, for DIEZ.
clc, clearvars
tr=sqrt((8*9999+1)-1)/2
t=0; tri4dig=char.empty;
for n=1:tr
t=t+n;
if t>999 && t<10000
tri4dig=[tri4dig ;char(string(t))];
end
end
for i=1:length(tri4dig)
if tri4dig(i,1)==tri4dig(i,4) ...
&& length(unique(tri4dig(i,:))) == 3
disp(tri4dig(i,:))
searchFor=[ tri4dig(i,3) tri4dig(i,2) ];
for j=1:length(tri4dig)
if tri4dig(j,2:3)==searchFor
disp([' ' tri4dig(j,:)])
end
end
end
end
finds 4-digit triangular numbers matching the pattern of SEIS, and for each of those numbers, finds triangular numbers whose middle two digits match the reverse of the SEIS number's middle digits:
(possible DIEZ indented under possible SEIS)
1081
1431
2346
1891
3403
9045
6216
1128
8128
6786
7875
9870
8128
2211
6216
E must be odd leaving only 6786 and 8128 to be SEIS. If the former, DIEZ must be 9870, as D cannot duplicate the 7 that is E. For a similar reason, if SEIS is 8128, then DIEZ can't be 2211. DIEZ also cannot be 6216, as then D would equal Z.
So SEIS = 6786 and DIEZ = 9870.
SIETE is then 687T7, with T chosen to make the SIETE prime.
Successive primes in that area are:
68711
68713
68729
68737
68743
68749
68767
68771
68777
68791
and only 68737 will do for SIETE.
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Posted by Charlie
on 2021-12-21 10:27:47 |
Hybrid solution
