Answer:
{1, 2, 4, 5, 6, 8, 10, 11, 12, 14, 15, 16, 19, 20, 23, 24, 25, 27, 28, 29, 31, 32, 33, 35, 36, 37, 39, 40, 41, 43, 44, 47, 48, 51, 52, 55, 56, 59, 60, 64, 68, 72, 74, 76, 78, 80, 82, 86, 90, 94, 98}
Step-by-step explanation:
The total number of pushups Bucky does is the sum sequence of scores in the game. The values in that sequence depend on the order of the goal types.
For example, consider a 2-goal game. Possible sequences of scores are ...
3, 6 (9 pushups)
3, 10 (13 pushups)
7, 10 (17 pushups)
7, 14 (21 pushups)
You can see that for a 1- or 2-goal game, the number of pushups cannot be any of ... 1, 2, 4, 5, 6, 8, 10, 11, 12, 14, 15, 16.
The list above is all of the numbers less than 100 that are numbers of pushups Bucky will never do in any game in which the goal values are either 3 or 7.
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Any game with 8 goals or more will have numbers of pushups more than 100.
