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(النص الأصلي) Comparison Sorting suggestion

I suggest a new game called Comparison Sorting.

Similarly to Coin Weighing, I suggest that the game starts with a series of objects of unknown weight, and the player may use a limited amount of comparisons. However, each side of the comparison may only have one object in it, and the objects are all of different weights. The player must put all of the objects in ascending order. After the player performs the comparisons and places the objects in the list, the game will then assign the objects as different numbers and if at some point one of the objects is greater than the next in the list, the game highlights a red '>' symbol at the wrong pair, then displays 'You lose' and offers the option to use LIFE power up, which restarts the level. If all the objects are less than the next, the game displays green '<' symbols between every consecutive pairs, and continues to the next level.

I suggest 10 levels, with the level number corresponding to the number of objects:

Level 1: 0 comparisons
Level 2: 1 comparisons
Level 3: 3 comparisons
Level 4: 5 comparisons
Level 5: 7 comparisons
Level 6: 10 comparisons
Level 7: 13 comparisons
Level 8: 16 comparisons
Level 9: 19 comparisons
Level 10: 22 comparisons

https://en.wikipedia.org/wiki/Comparison_sort#Number_of_comparisons_required_to_sort_a_list

If the game detects that the comparisons do not adequately narrow down the set of possible permutations, then the game will always display the wrong permutation. For example, level 10 starts with 3628800 possible permutations and 22 comparisons remaining. If the player compares a and b, then both a>b and a<b have 1814400 permutations each. If the first comparison was a<b, and the player then compares b and c, then there are 604800 permutations for the case a<b<c, and 1209600 permutations for the case a<b>c, and 20 comparisons remaining. Since 20 comparisons can theoretically have no more than 2^20 (1048576) different results, the game will choose the a<b>c option, which has 1209600 permutations, making it impossible for 20 comparisons to always determine the sorted list, the game will then choose comparison results in such a way that does not narrow down to 1 permutation, and the game will then fill in the objects with the numbers 1 to 10 in such a way that is not sorted, and display 'You lose'.

If the player completes all 10 levels, the game will display 'You win', and the leaderboard will display 'all clear'.

The ANSWER power up will display comparisons that always narrow down to 1 permutation.

Mastery criteria should be the following:

2 stars — level 5
3 stars — level 7
4 stars — level 9
5 stars — all clear