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(由 Microsoft 翻译) 我推荐一个叫做 Comparison Sorting 的新游戏。
与 Coin Weighing 类似，我建议游戏从一系列重量未知的物体开始，玩家可以使用有限数量的比较。但是，比较的每一侧可能只有一个对象，并且这些对象都具有不同的权重。玩家必须按升序排列所有对象。在玩家进行比较并将对象放入列表后，游戏会将对象分配为不同的数字，如果在某个时候其中一个对象大于列表中的下一个对象，游戏会在错误的对上突出显示一个红色的“>”符号，然后显示“你输了”并提供使用 LIFE 道具的选项。 这将重新启动该级别。如果所有对象都小于下一个对象，游戏将在每个连续对之间显示绿色的“<”符号，并继续进入下一级别。
我建议 10 个级别，级别编号对应于对象的数量：
级别 1：0 个比较
第 2 级：1 个比较
第 3 级：3 次比较
第 4 级：5 次比较
第 5 级：7 个比较
第 6 级：10 次比较
第 7 级：13 个比较
第 8 级：16 个比较
第 9 级：19 个比较
第 10 级：22 个比较
https://en.wikipedia.org/wiki/Comparison_sort#Number_of_comparisons_required_to_sort_a_list
如果游戏检测到比较没有充分缩小可能的排列集，则游戏将始终显示错误的排列。例如，级别 10 开始时有 3628800 个可能的排列，还剩下 22 个比较。如果玩家比较 a 和 b，则 a>b 和 a<b 各有 1814400 次排列。如果第一次比较是 a<b，然后玩家比较 b 和 c，则情况 a<b<c 有 604800 次排列，情况 a<b>c 有 1209600 次排列，还剩下 20 次比较。由于 20 次比较理论上可以产生不超过 2^20 （1048576） 个不同的结果，因此游戏将选择 a<b>c 选项，该选项有 1209600 个排列，使得 20 次比较不可能总是确定排序列表，然后游戏将以不缩小到 1 个排列的方式选择比较结果， 然后游戏将以未排序的方式用数字 1 到 10 填充对象，并显示 'You lose'。
如果玩家完成所有 10 个级别，游戏将显示“您赢”，排行榜将显示“全部清除”。
ANSWER powerup 将显示始终缩小到 1 种排列的比较。
精通标准应为：
2 星 — 5 级
3 星 — 7 级
4 星 — 9 级
5 星 — 全部清除
与 Coin Weighing 类似，我建议游戏从一系列重量未知的物体开始，玩家可以使用有限数量的比较。但是，比较的每一侧可能只有一个对象，并且这些对象都具有不同的权重。玩家必须按升序排列所有对象。在玩家进行比较并将对象放入列表后，游戏会将对象分配为不同的数字，如果在某个时候其中一个对象大于列表中的下一个对象，游戏会在错误的对上突出显示一个红色的“>”符号，然后显示“你输了”并提供使用 LIFE 道具的选项。 这将重新启动该级别。如果所有对象都小于下一个对象，游戏将在每个连续对之间显示绿色的“<”符号，并继续进入下一级别。
我建议 10 个级别，级别编号对应于对象的数量：
级别 1：0 个比较
第 2 级：1 个比较
第 3 级：3 次比较
第 4 级：5 次比较
第 5 级：7 个比较
第 6 级：10 次比较
第 7 级：13 个比较
第 8 级：16 个比较
第 9 级：19 个比较
第 10 级：22 个比较
https://en.wikipedia.org/wiki/Comparison_sort#Number_of_comparisons_required_to_sort_a_list
如果游戏检测到比较没有充分缩小可能的排列集，则游戏将始终显示错误的排列。例如，级别 10 开始时有 3628800 个可能的排列，还剩下 22 个比较。如果玩家比较 a 和 b，则 a>b 和 a<b 各有 1814400 次排列。如果第一次比较是 a<b，然后玩家比较 b 和 c，则情况 a<b<c 有 604800 次排列，情况 a<b>c 有 1209600 次排列，还剩下 20 次比较。由于 20 次比较理论上可以产生不超过 2^20 （1048576） 个不同的结果，因此游戏将选择 a<b>c 选项，该选项有 1209600 个排列，使得 20 次比较不可能总是确定排序列表，然后游戏将以不缩小到 1 个排列的方式选择比较结果， 然后游戏将以未排序的方式用数字 1 到 10 填充对象，并显示 'You lose'。
如果玩家完成所有 10 个级别，游戏将显示“您赢”，排行榜将显示“全部清除”。
ANSWER powerup 将显示始终缩小到 1 种排列的比较。
精通标准应为：
2 星 — 5 级
3 星 — 7 级
4 星 — 9 级
5 星 — 全部清除
(原文) 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
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
作者 Piotr Grochowski
2024-12-19 00:59:52
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