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11 Nov 2024, 06:16
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Cannot Start the Second Game: Tsui
Must Start the Fourth Game: Lavanco
A baseball manager must choose both a starting pitcher from Rincon, Salamanca, Tsui, Vereen, and Wells, and a starting catcher from Gaston, King, and Lavanco for each of the team’s next five scheduled games. Per league restrictions, no catcher can play consecutive games and each pitcher may only pitch once every five games. Based on his own insights, the manager has determined that Salamanca must pitch to King, that if Tsui pitches to Lavanco, then Rincon must pitch to Gaston, that Vereen must pitch in the fourth of the five games, and that Wells’ start and Lavanco’s second start must come after Salamanca’s start.
If one of the catchers gets unexpectedly injured in practice becoming unable to play in any of the five games, but all other restrictions remain in place, select a pitcher who cannot pitch in the second game and a catcher who must catch the fourth game. Make only two selections, one in each column.
If one of the catchers gets unexpectedly injured in practice becoming unable to play in any of the five games, but all other restrictions remain in place, select a pitcher who cannot pitch in the second game and a catcher who must catch the fourth game. Make only two selections, one in each column.
| Cannot Start the Second Game | Must Start the Fourth Game | |
| Gaston | ||
| King | ||
| Lavanco | ||
| Rincon | ||
| Tsui | ||
| Wells |
ShowHide Answer
Official Answer
Cannot Start the Second Game: Tsui
Must Start the Fourth Game: Lavanco
11 Nov 2024, 06:17
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Official Solution:
Plug G into the 4th and 2nd catcher spot. Because L's second start must come after S's start, then L must be 1st, 3rd, and 5th, but then because S must pitch to K this outcome isn't possible as there are no spots left for S nor K and each pitcher must pitch one of the games. Therefore, G cannot go 4th.
Now, if K goes 4th he must also go 2nd and S must go second with K, and as previously determined L must go 1st, 3rd, and 5th, which dictates that T must pitch to L which means that R must pitch to G, but there are no more spots for G to catch, so K cannot be 4th.
Therefore, L must catch the 4th and 2nd games, and K must catch games 1, 3, and 5. Therefore, T cannot pitch game 2 to L, because then R must pitch to G and there are no spots for G.
Correct answer:
Cannot Start the Second Game "Tsui"
Must Start the Fourth Game "Lavanco"
TetyanaRokobit
Use initials to simplify the consideration of the eight different players. Start by considering game 4 which V must pitch. Because there are only two catchers available due to the injury, whoever catches 4th must catch 2nd to avoid any consecutive starts.
Plug G into the 4th and 2nd catcher spot. Because L's second start must come after S's start, then L must be 1st, 3rd, and 5th, but then because S must pitch to K this outcome isn't possible as there are no spots left for S nor K and each pitcher must pitch one of the games. Therefore, G cannot go 4th.
Now, if K goes 4th he must also go 2nd and S must go second with K, and as previously determined L must go 1st, 3rd, and 5th, which dictates that T must pitch to L which means that R must pitch to G, but there are no more spots for G to catch, so K cannot be 4th.
Therefore, L must catch the 4th and 2nd games, and K must catch games 1, 3, and 5. Therefore, T cannot pitch game 2 to L, because then R must pitch to G and there are no spots for G.
Correct answer:
Cannot Start the Second Game "Tsui"
Must Start the Fourth Game "Lavanco"
12 Dec 2024, 16:11
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Bunuel or bb
Could you possibly explain this better than the official solution? I am still confused because it says, "Therefore, L must catch the 4th and 2nd games, and K must catch games 1, 3, and 5." Since S has to pitch to K, how would K catch 1, 3, 5 considering pitchers are only allowed to play every 5th game? Is there a clearer and more straightforward path to figuring out the answer than explained above?
Could you possibly explain this better than the official solution? I am still confused because it says, "Therefore, L must catch the 4th and 2nd games, and K must catch games 1, 3, and 5." Since S has to pitch to K, how would K catch 1, 3, 5 considering pitchers are only allowed to play every 5th game? Is there a clearer and more straightforward path to figuring out the answer than explained above?
