Determine the smallest integer N such that the decimal representation of N contains only the digits 0 and 1, and there are 8 distinct integers A,B,C,D,E,F,G,H where the 8 quotients N/A, N/B, N/C, ..., N/H are all pandigital integers.
That is, each quotient contains each of the digits 0 to 9 exactly once. For example, 1001100111111 / 373 = 2683914507.
There must be nine 1's to be divisible by 9.
clearvars,clc
ct=0;
for numZeros= 1:6
s=[repmat('0',[1,numZeros]) repmat('1',[1,9])];
sSet=uniqueperms(s);
for i=1:size(sSet,1)
ss=sSet(i,:);
if ss(1)~='0'
n=str2double(sSet(i,:));
dv=divisors(n);
ct=0;
for j=1:length(dv);
s=num2str(n/dv(j));
if length(s)==10 && length(unique(s))==10
fprintf('%15s %7d %12d\n',sSet(i,:),dv(j),n/dv(j))
ct=ct+1;
end
end
if ct>0
disp(ct)
end
end
end
end
finds
N divisor quotient
11111111010 9 1234567890
1
111111110100 18 6172839450
111111110100 36 3086419725
111111110100 45 2469135780
111111110100 90 1234567890
4
1001100111111 373 2683914507
1
1111111101000 180 6172839450
1111111101000 225 4938271560
1111111101000 360 3086419725
1111111101000 450 2469135780
1111111101000 900 1234567890
5
10011001111110 1865 5367829014
10011001111110 3730 2683914507
2
10110001101111 1849 5467821039
1
10111010110110 1183 8546923170
1
10111101111000 3725 2714389560
1
11011010111010 10595 1039264758
1
11011110100110 1445 7620145398
1
11101101110100 2545 4361925780
1
11110011100101 1319 8423056179
1
11110110101100 1615 6879325140
1
11111111010000 1125 9876543120
11111111010000 1800 6172839450
11111111010000 2250 4938271560
11111111010000 3600 3086419725
11111111010000 4500 2469135780
11111111010000 5625 1975308624
11111111010000 9000 1234567890
7
100110011111100 18650 5367829014
100110011111100 37300 2683914507
2
100111010110101 39423 2539406187
100111010110101 66623 1502649387
2
100111011101010 31598 3168270495
1
100111100111010 47746 2096743185
1
101100011011110 18490 5467821039
1
101110011011100 13148 7690143825
1
101110101101100 11830 8546923170
1
101111011110000 37250 2714389560
1
101111100100101 40677 2485706913
1
110011110110010 89109 1234567890
1
110101110001110 26655 4130598762
1
110110101110100 105950 1039264758
1
110110110100110 18234 6038724915
1
110111101001100 14450 7620145398
1
111011011101000 25450 4361925780
1
111100111001010 13190 8423056179
1
111100111101000 14875 7468915032
1
111101000110110 25434 4368207915
1
111101101011000 16150 6879325140
1
111110010001011 15757 7051469823
1
111111001000110 30895 3596407218
1
111111010001100 88345 1257694380
1
111111110100000 11250 9876543120
111111110100000 18000 6172839450
111111110100000 22500 4938271560
111111110100000 28125 3950617248
111111110100000 36000 3086419725
111111110100000 45000 2469135780
111111110100000 56250 1975308624
111111110100000 90000 1234567890
8
The number underneath each grouping (or single) shows how many divisors work for that number composed of zeros and ones.
The final grouping, for 111111110100000, shows 8 divisors (11250, 18000, 22500, 28125, 36000, 45000, 56250, 90000) which result in a quotient that's such a pandigital.
Edited on May 27, 2024, 2:04 pm
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Posted by Charlie
on 2024-05-27 14:00:22 |
computer solution