Does your house have a basement?

Logic Level 4

10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 20 , 22 , 24 , 31 , 100 , ? , 10000 \large 10, 11, 12,13, 14, 15, 16, 17, 20, 22, 24, 31, 100, ? , 10000

Which number can replace the question mark in the above sequence?

Hint: 16.


The answer is 121.

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1 solution

Nihar Mahajan
Jul 1, 2015

Each number is 16 in a number system with a different base, starting with base 16 and continuing with bases in descending order, ending with base 2.

16 16 in base 16 16 is 10 10

16 16 in base 15 15 is 11 11

16 16 in base 14 14 is 12 12

16 16 in base 13 13 is 13 13

16 16 in base 12 12 is 14 14

16 16 in base 11 11 is 15 15

16 16 in base 10 10 is 16 16

16 16 in base 9 9 is 17 17

16 16 in base 8 8 is 20 20

16 16 in base 7 7 is 22 22

16 16 in base 6 6 is 24 24

16 16 in base 5 5 is 31 31

16 16 in base 4 4 is 100 100

16 16 in base 3 3 is 121 \boxed{121}

16 16 in base 2 2 is 10000 10000

Hence , the answer is 121 121 . :)

I guessed 16 then gave up. :P

Brock Brown - 5 years, 10 months ago

Ohhhh......nice question Nihar!!! Somehow the sequence looks kinda ordinary at the beginning where the numbers were in running order then after that they suddenly became ridiculously big!!! @Nihar Mahajan Anyway is there any significance in the title of your question 'Does your house have a basement'? Just wondering if it is in any way relevant cos I was trying to use it to help me get the answer!! It would be good if you can share with me!!

Noel Lo - 5 years, 11 months ago

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I think he's just playing on the idea of different number bases (basements).

Ryan Tamburrino - 5 years, 11 months ago

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Yeah , correct.

Nihar Mahajan - 5 years, 11 months ago

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@Nihar Mahajan Wonderful problem! Did you make this question yourself? ....I think this question can also fit into Number Theory or Computer Science.

Rajdeep Bharati - 5 years, 7 months ago

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@Rajdeep Bharati No , this problem was given to me by my friend.

Nihar Mahajan - 5 years, 7 months ago

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@Nihar Mahajan Hello @niharmahajan, nice question, but could you please explain what does base means(what you stated above).. I dont really understand it.. Thx

Victor Zhang - 5 years, 3 months ago

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@Victor Zhang We usually follow a base 10 system (decimal system), where numbers are from 0 to 10. There are other systems too; i.e, binary (base 2), hexadecimal (base 16), etc.

Rajdeep Bharati - 5 years, 3 months ago

a nice question! almost gave up then your title helped me solve it! :p

Gokul Kumar - 5 years, 10 months ago

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