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Mittwoch, 16. September 2020
Vulcan's day

4 min 06sec

5 min 0sec

1 min 53 sec

Question how many possibilities are existent for a futoshiki of nxn version where no condition via inequalities is existent

Answer : this is the product of all n! from 1 to n

Proof via induction

for n = 1 this is 1 ! it's clear

Now look at the table for an example 1 to 2

* 2 * 1 *
* 1 * 2 *

Everywhere where the * ist placed the 3 can be inserted
for once in a row and in a column.

So these are 3 *2 , possiblities , so this is exactly the factor 3!. Which we desired. The proof is now clear and left to the reader.

Note for 2 there are just 2 possiblilities

1 2
2 1
and
2 1
1 2

So the proof should now be clear and follows from peano and induction.

Other thoughts , like the amount of possible sudoku combinations , follow the pattern of a placeholder like this , if they are implemented in a clever way, and are as trivial and easy.

5 min 20 sec, 12 x 12 Daily Network, no wrap, easy

3 min 21 sec , sky hard 5x5

5 min 5 sec

Greetings

B__k_s K_f_r

top_os_b am 16. September 20  |  Permalink  |   | 



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