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Defective Clock

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BMAD has a defective clock in his room. The clock is digital, and some of the seven bars on its units digit are broken. A bar that works is on when it should be and off when it should be, whereas a broken bar is off regardless of the time.
a) BMAD enters his room and glances at his clock. He knows how many bars are broken but he doesn't know which ones they are. He immediately knows for sure what the time is.
b) BMAD enters his room and glances at his clock. He knows which bars are broken and immediately knows for sure what the time is.
c) BMAD enters his room and knows which bars are broken. He stares at his clock for 60 seconds. Now he knows for sure what time it is.
d) BMAD enters his room. He knows how many bars are broken but he doesn't know which ones they are. He stares at his clock for 60 seconds. Now he knows for sure what time it is.
In each of these four scenarios, what is the maximum number of broken bars, and which might it/they be?
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Posted (edited) · Report post

a) Three


b) Five
c) Six

d) Six

Edited by gavinksong
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Posted · Report post

upper left bar can not be broken for 3 & 9
lower left bar can not be broken for 5 & 6
upper right bar can not be broken for 5 & 9
middle bar can not be broken for 8 & 0

1)1-You can tell time with any broken top or bottom or lower right
2)2-You can tell time with any broken top or bottom + lower right
3)3-You can tell time waiting what is next to 4 or 9 with broken top, bottom & lower right
4)4-The middle is also broken

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Posted · Report post

4) 4- lower left & right & top & bottom

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a) Three (ex. if the actual time was 8 and the clock showed a backwards 4, BMAD would be able to tell the time immediately)


b) Five (ex. if the actual time was 5 or 6 and the only functioning bars were the bottom-left and the top-right, BMAD would be able to tell the time immediately)
c) Six (ex. if the actual time when BMAD entered the room was 5 or 6 and the only functioning bar was the top-right, BMAD would be able to tell the time after 60 seconds)
d) Six (ex. if the actual time when BMAD entered the room was 6, BMAD would be able to tell the time after 60 seconds because the top-right bar would light up when the time became 7)
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