perplexus.info :: Just Math : A permutation puzzle

A permutation puzzle (Posted on 2006-09-20)

Determine the number of permutations (p₁, p₂,...p₇) of 1,2, ...7; such that for all k 1≤k≤6, (p₁, p₂,... p_k) is not a permutation of (1,2, ...k); i.e., p₁≠1; (p₁, p₂) is not a permutation of (1,2), etc.

What would be the answer if we specify 1≤k<6 instead?

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

computer solution

| Comment 5 of 6 |

a=[1 2 3 4 5 6 7]

p=perms(a); count=0;

for r=1:size(p)

p0=p(r,:); good=true;

for k=1:6

pk=p0(1:k);

pt=a(1:k);

if pt==sort(pk)

good=false;

break

end

if good

count= count+1;

end

count

count =

3447

Part 2:

If instead we use

for k=1:5

we get

count =

3908

Posted by Charlie on 2020-11-24 12:44:13

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