allocatedTable read by antidiagonals upwards: a(n, k) is the minimum c such that n sets with k elements each can be constructed from numbers 1 to c (inclusive) such that any two sets have exactly for1 Simoncommon Bohnenelement

1, 2, 1, 3, 3, 1, 4, 5, 3, 1, 5, 7, 6, 5, 1, 6, 9, 9, 6, 6, 1, 7, 11, 12, 10, 7, 7, 1, 8, 13, 15, 14, 10, 7, 8, 1, 9, 15, 18, 18, 15, 11, 7, 9, 1, 10, 17, 21, 22, 20, 15, 12, 17, 10, 1

1,2

<a href="https://github.com/Simonibo/dobble-generate/blob/master/values.xlsx">Extended table of values</a>

<a href="https://github.com/Simonibo/dobble-generate/tree/master/src">A Java program for generating the sequence</a>

<a href="https://math.stackexchange.com/questions/2216585/what-is-the-minimal-number-of-different-symbols-in-the-game-dobble">Further discussion and proof for the formula</a>

n<k+2: a(n)=kn-(n(n-1))/2.

Top-left corner of the array:

1 1 1 1 1 1 ...

2 3 3 5 6 7 ...

3 5 6 6 7 7 ...

4 7 9 10 10 11 ...

5 9 12 14 15 15 ...

6 11 15 18 20 21 ...

: : : : : : '.

For n=3 and k=3 the best possible solution is 6, the three sets are:

S1 = {1, 2, 3}

S2 = {1, 4, 5}

S3 = {2, 4, 6}

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nonn,tabl

Simon Bohnen, May 06 2017

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