Prison Break

Number Theory Level 3

You’re in prison planning your escape. You’ve discovered that every Sunday, the guards watch a football game and you have time to dig your escape tunnel.

Today is Thursday. If you can dig 5 meters every Sunday and you need 125 meters more in your tunnel to make it to freedom, how many days remain until you can make your escape?

Image source: Leigh Wiener

175 178 171 173

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Arron Kau by Arron Kau

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2 solutions

Arijit Banerjee
Apr 15, 2014

Well at first it wud seem that the answer is 178...but it is not ... from 1st Sunday( The Sunday which is coming after the thursday) to the second Sunday, length of the tunnel dug out is 10m so to calculate the number of sundays we have to exclude 5 metres at first from 125m . So number of Sundays is 24 . Now the number of days is 24 * 7 = 168 days . Now we've to add 3 because after Thursday there are only 3 days "friday " , "Saturday" & "Sunday" . So answer is 171 .

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Anik Mandal
Jun 5, 2014

OK, we need 125/5 =25 Sundays to dig the tunnel which means that we need 24 weeks plus the 3 days remaining until the 1st Sunday. Today is Thursday. So the 1st Sunday will be 3 days later. So the total number of days we need to dig the tunnel = 3 +7(the number of days/ week)*24 = 171 day

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