What day is it?

Number Theory Level 1

If today is a Tuesday, then what day of the week will it be in 100 days?

Saturday Tuesday Monday Wednesday Sunday Thursday Friday

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Stewart Feasby by Stewart Feasby , 23, United Kingdom

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5 solutions

Vinay Varma
May 9, 2015

divide 100 by 7... we get quotient as 14 and remainder as 2... so from tuesday the second day is thursday

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Moderator note:

Yes correct, this problem is a simpler version to a problem we had awhile ago.

Stewart Feasby
May 1, 2015

As today is a Tuesday, then after 7 days, it will still be a Tuesday as there are always 7 days in a week.

Therefore it is correct to say that after 7 n 7n days, the day will not have changed. As the greatest multiple of 7 less than 100 = 98, i.e. n = 14 n=14 , Then the day must be just two days later as 100 − 98 = 2 100-98=2 : M o n d a y , T u e s d a y , W e d n e s d a y , T h u r s d a y , F r i d a y , S a t u r d a y , S u n d a y Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday Therefore thursday is the answer.

T h u r s d a y \boxed {Thursday}

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Moderator note:

Correct! Bonus question: If today is a Tuesday, for whole number n n , is it possible that it is still a Tuesday after 1 0 n 10^n days?

yes . 10*10 .....n times is an integer.

Manas K. Chowdhury - 6 years, 1 month ago

Challenge Master: No it is not possible after 1 0 n 10^n days as to still be a Tuesday the number of days past must be equal to a multiple of 7, whereas 1 0 n 10^n is the same as ( 5 × 2 ) n (5\times2)^n . This shows that every integer value of n will produce a value that is not a multiple of 7, as that number will comprise of solely 5s and 2s as its prime factors.

Stewart Feasby - 6 years ago
Bharat Naik
May 15, 2015

since a week has 7 days figure out the closest multiple of 7 to 100.we get it as 14 weeks i.e;98 days.that means the 98th day is a tuesday then 100th day will be two days after it i.e; thursday.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Moderator note:

Correct! Bonus question: What would the answer be if I replace the number 100 by 10,000?

the closest multiple of 7 to 10,000 is 1428 i.e.,9996 ..so, 9996 subtracted from 10,000 would be 4.four days after tuesday is saturday

swaathi rameshwar - 6 years, 1 month ago

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correct its saturday

Bharat Naik - 6 years ago

it would be a saturday

Bharat Naik - 6 years ago

first divide 100 by 7 and it leave remender 2 so, tuesday + 2 days = thursday :)

0 Helpful 0 Interesting 0 Brilliant 0 Confused
David E Mione
May 16, 2015

Simply divide 100/7 and you get 14.29 (rounded). So figure the 14 equals to it being on a Tuesday, the .2 is the extra amount of time, which means the day has to be Thursday.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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