Prison Break

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

$**1^{st} solution**$

From the first Thursday to Sunday, you can dig 5 m. -> $3$ days required.

So you need to dig 120 m. more = $\frac{120 m.}{5 m./sundays} = 24$ more Sundays.

You need 24 more weeks = $24\times 7 = 168$ days.

Therefore, the number of days = $3+168=\boxed{171}$ .

$**2^{nd} solution**$

You can think that you need $\frac{125 m.}{5 m./sundays} = 5$ Sundays = $25\times 7 days = 175$ days.

But this starts from the past Sunday to the first Sunday you start digging, so you need to exclude Sunday to Thursday.

From past Sunday to Thursday, takes 4 days.

Therefore, the number of days = $175-4=\boxed{171}$ .

since today is thursday therefore he would dig first 5 meters in first sunday..(thus is first 3 days..) now 120 meters left and would be dug on each sunday..(hence no. of sundays = 120/5=24) >therefore no. of days = 3+ 24*7 = 171

125/5 = 25 Sundays needed. Today is Thursday so 3 more days to Sunday. 24*7 = 168 + 3 = 171

This is meant for those who love to code :)

//include iostream statement here

//compile with any c++ compiler

using namespace std;

int main () {

int WEEK [] = {1, 2, 3, 4, 5, 6, 7};

int today = WEEK [4];

int daysPassed (0), tunnelDug (0), counter (4);

while (tunnelDug != 125) {

    if (today == 7) { tunnelDug += 5; }

    daysPassed++;

    counter++;

    if (counter > 6) { counter = 0; }

    today = WEEK [counter];

}

cout << daysPassed << endl;

return (0);

}

The answer is 171 days

có 25 ngày chủ nhật => có 24 tuần cộng thêm 3 ngày từ thứ 6 đến chủ nhật của tuần hiện tại kết quả là 7*24+3=171 hihihi ^^

after 3 days is sunday and i dug 5m. Now 120 m remaining 125-5=120 every sunday i.e. every i dig 5m as I have only one day in week to do so no. of week required to dig 120m= 120/5= 24 no. of days= 7*24=168 total num of days= 168+3 =171

WE NEED 125/5=25 SUNDAYS. THAT WOULD BE 25*7=175 DAYS BUT SINCE MONDAY TO THURSDAY OF THE FIRST WEEK ARE NOT COUNTED(4 DAYS), THE NO. OF DAYS IS 175-4=171

It's 7 days to Sunday after coming Sunday. Therefore: 3 days to coming Sunday + 7 days to coming 24 Sundays = $3 + (7 \times 24) = 171$

I almost got the wrong ans. if I did not recheck. I had added extra days. Got to be careful with these No. of days questions. I always test for a small days before extending the logic to larger numbers . This strategy is well-planned and always helps. The answer is 171!

You would need 25 Sundays to dig the tunnel. Then you must wait Friday and Saturday. This Sunday is one of the Sundays and 24 more Sundays (at the end of 7 day weeks) to dig the tunnel. That would be 3 + 7(24) = 171 days until freedom.

sine we need 25 sundays to dig 125 meter... therefore total number of days = 175... but the day starts from friday as today itself is thursday... hence the required no. of days is 171

Today is Thursday. We can dig 5 meters in one Sunday. So number of Sundays required to make the complete tunnel of length 125 meters is 125/5, which is equal to 25 Sundays.Now in between 2 consecutive Sundays there are 6 days .So in between 25 Sundays there are a total of 24x6 days=144 days. Now the total number of days from today till freedom is 144+25+2days =171 days. + 2 days because today is Thursday and tomorrow and day after tomorrow is also counted which is Friday and Saturday.

On each Sunday, I can dig 5 meters

So to dig 125 meters, I need 125/5 = 25 Sundays.

And 25 Sundays will mean 25 weeks, i.e. 25 X 7 days = 175 days.

but it is already a Thursday in the present week, meaning 4 days have already gone by.

So no. of days remaining = `175 - 4 = 171

25 sundays will come in 24 weeks plus 3 days for current week i.e., $24*7+3=171$

if we start from sunday then we are 3 days in advance and then 120/5=24 weekss are left. so no of days that remain until escape=(24*7)+3=171.

Friday to Sunday = 3 days, On sunday, I'll dig 5 m. Rest 120 m will be required. 120 m will be dig in next (120/5 = 24) weeks. total days to escape = (24 * 7 + 3) days = (168 + 3) days = 171 days

It is given that you can dig $5$ meters every Sunday. You need a total of $125$ meters, so:

$\frac{125}{5} = 25$

You need a total of 25 Sundays to complete the mission. In those 25 Sundays

$(25-1) \cdot 7 = 24 \cdot 7 = 168$

there are $168$ days.

However, today is just Thursday. So, until the first Sunday, there are still $3$ days for you to wait. Thus

$168 + 3 = \boxed{171}$

All in all, $171$ days remain before you can escape.

Today is thursday. The 4th day comes the first sunday where he digs first 5 metres. So then we are left with 120 metres to dig.

Each sunday he digs 5 metres, hence 120/5 = 24 sundays. Every week has 7 days . so 24 * 7 =168 days .

So finally first 4 days plus 168 = 168 + 4 = 172. But he escapes on 172nd day. so 171 days left. :)

You have 3 days until the next Sunday, because it is Thursday. For every Sunday after that it will be 7 days. Each Sunday you can dig 5 meters so 125-the 5 from the 3 days/5=24. 24x7=168 days. Now add the 3 days and get 171. The question asks how many days until you can make your escape so 171 days.

5 meters per week

days left in this week - 3 ( F S S )

so 120 more meters after this week

120/5 = 24 is the number of weeks required after this week

∴ days required = 3 + 24 X 7 = 171

good day ! :)

Given that today is Thursday and I can only dig 5 meters of the tunnel every Sunday and have 125 m digging left. So, till the coming Sunday, we have the coming days (Friday, Saturday and then comes Sunday). So, we have already elapsed $\boxed{3}$ days and now after digging on that Sunday, he has left $125-5=120$ m.

Now, each week has 7 days and he can digs $5$ m on each Sunday, i.e, once a week, so the remaining part will be dug in $\frac{120}{5}=24 \text{weeks} = 24\times 7 \text{days} = 168$ days. But, the $3$ days elapsed at the start is also to be counted in the no. of days.

So, total no. of days till escape $=168+3 = \boxed{171}$

(125/5)*7-4=171

I wrote this:

Monday Tuesday Wednsday Thursday Friday Saturday Sunday . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 . . . . . . .1. . . . . . . 2 . . . . . . 3 . . . 4 . . . . . . 5 . . . . . . . .6 . . . . . . . . . .7 . . . . . . 8 . . . . . . . 9 . . . . . . 10 . . . 11 . . . . . 12 . . . . . . . 13 . . . . . . . . 14. . . . . .15 . . . . . .16 . . . . . . 17 ... And so on...

So then I saw a pattern:

3 days - 120 meters left (Considering you dug that day) 10 days - 115 left 17 days - 110 left .... x days - 0 left

So... how many times you need to add 5 to get 120? by multiplication: 5 24 = 120 Then... I've multiplied 24 7 = 168 (7 because only on sundays you can dig and from sunday to sunday are 7 days) and that's the number of days to advance 120 meters.

And now I've just added 3 more days and TA-DA! there it is the answer.

168 days + 3 days = 171 days

It will require 25 Sundays more to dig 125m. And there are 24 seven day periods between these sundays. Total duration = ( to First Sunday) +24 * 7 = 3+168 =171

You start on Thursday so till Sunday you have 3 days. Then to dig up he need 25 Sundays. Out of 25, 24 corresponds to week, so 24*7=168 days. and on 25th Sunday he is out. So Total days 168+3 =171.

First divide 125/5=25 sundays needed to dig for the escape. If today is Thursday we have 3 days to finish the week( Friday, Sat, Sun) and sunday we decrease 1 from 25. Now we have 24 sundays* 7 days of the week= 168 days + initial 3 days= 171.

Thus, in 171 days you can make your escape.

Calculated guess- Well I didnt actually solve it. I made a calculated guess. When I read the problem I got a feeling that if at times people may add an extra 7 days because they may not realise that they can escape the moment the tunnel is finished and may end up waithing for the next sunday. The person who has asked this question may have this thing in mind and thus would have the options in such a way that atleast one of the options "ans + 7" there was only one such pair (171 and 178) so I went with 171

3 Days to first Sunday + 24 weeks time to dig last 5 meter = 3+(24*7)=171.

See 125m means 25 Sundays (5m on every sunday) Which indeed means 24 full weeks. Now this was planned on a thursday so 25th sunday is sunday of the first week Now 24 full weeks imply 168 days and 3 more days are days after the first thursday which gives a total of 171days.

Tunnel length = 125 m; We can dig 5m every Sunday. so we need 125/5=25 Sunday. In between 25 Sundays 24 weeks are there, means 24X7 = 168 days are there. Today is Thursday so from today to coming Sunday there is 3 days more so total 168+3 = 171 days remain to escape. Thank you.

Days remaining till first sunday = 2 No. of sundays required to dig = 125/5 = 25 total days remaining = 2 + (25-1)*7 + 1 = 171

125m/5m per day = 25 sunday 1 week =7day 25*7=(175day+3(Thursday)-7(25th Sunday) =171 days remaining