Grundy numbers for 0:0,1:0,2:0,3:1,4:0,5:2,6:3,7:4,8:0 Grundy number for n>=9 = n-4

Using Grundy Numbers following code:

def stonePiles(arr): maps = {0:0,1:0,2:0,3:1,4:0,5:2,6:3,7:4,8:0} res = 0 for ele in arr: if ele<=8: res^=maps[ele] else: res^=(ele-4) if res == 0: return 'BOB' else: return 'ALICE'

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Here is Stone Piles problem solution in Python java C++ and C programming - https://programs.programmingoneonone.com/2021/07/hackerrank-stone-piles-problem-solution.html

With test case: 6 piles. If Alice divide to: 2,4 . So She will win. But if she divide to: 1,2,3. So she will lost.

In the sample last test case:
1 8 The output says BOB win When Alice start: 8 -> 1,3, 4 Bob cannot break any and should loose Is it?