Evaluate the quantity of 4-digit numbers such that:
a. Use only 3 digits: 1,2 & 3.
b. None of its neighboring digits differ by 2.
Same question for numbers of 5 and 6 digits- still using only 1,2,3.
Enjoy!
clearvars,clc
global sz ct no lv ct2
sz=4; ct=0; lv=0; ct2=0;
no=[];
addon
ct
ct2
function addon
global sz ct no lv ct2
lv=lv+1;
saveno=no;
for i=1:3
chgd=false;
if length(no)==0
no=i;
chgd=true;
else
if abs(i-no(end))~=2
no=[no i];
chgd=true;
end
end
if chgd
if length(no)==sz
ct=ct+1;
if length(unique(no))==3
ct2=ct2+1;
fprintf('%d%d%d%d *\n',no)
else
fprintf('%d%d%d%d\n',no)
end
else
addon
end
end
no=saveno;
end
lv=lv-1;
end
finds 41 such 4-digit numbers, 10 of which use exactly all three of the allowable digits, marked with an asterisk below:
1111
1112
1121
1122
1123 *
1211
1212
1221
1222
1223 *
1232 *
1233 *
2111
2112
2121
2122
2123 *
2211
2212
2221
2222
2223
2232
2233
2321 *
2322
2323
2332
2333
3211 *
3212 *
3221 *
3222
3223
3232
3233
3321 *
3322
3323
3332
3333
ct =
41
ct2 =
10
Allowing the size of the number to change, not showing each individual case, just the statistics:
digits count count using all
three digits
3 17 2
4 41 10
5 99 36
6 239 112
7 577 322
8 1393 882
9 3363 2340
10 8119 6072
11 19601 15506
12 47321 39130
The 17 for 3-digit numbers are:
111
112
121
122
123 *
211
212
221
222
223
232
233
321 *
322
323
332
333
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Posted by Charlie
on 2023-07-24 11:58:42 |
computer solution
