Question

Find the missing number in the
following sequence:
10, 11, 12, 13, 14, 15, 16, 17,
20, 22, 24, 31, 100, ?, 10000
Hint: The missing number is in
ternary notation.​

Answer 1

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

To find : Missing number

Solution:

10 =  1 * 16¹ + 0 * 16⁰ = 16

11 = 1 * 15¹ +  1* 15⁰= 16

12 =  1 * 14¹ +  2* 14⁰ = 16

13 =  1 * 13¹ + 3 * 13⁰ = 16

14 = 1 * 12¹ +  4* 12⁰= 16

15 =  1 * 11¹ +  5* 11⁰ = 16

16 =  1 * 10¹ +  6* 10⁰ = 16

17 =  1 * 9¹ +  7* 9⁰ = 16

20 =  2 * 8¹ +  0* 8⁰ = 16

22 =  2 * 7¹ +  2* 7⁰ = 16

24 =  2 * 6¹ +  4* 6⁰ = 16

31 =  3 * 5¹ +  1* 5⁰ = 16

100 = 1 * 4² + 0 * 4¹ + 0*4⁰ = 16

121 =  1 * 3²  + 2*3¹ + 1*3⁰ = 16

10000 = 1 * 2⁴ + 0 * 2³ + 0 * 2² + 0 * 2¹ + 0 * 2⁰ = 16

This sequence is all numbers 16 with reducing base from  16  to 2

Missing number is  16 in base  3

          16

     _______

  3       5      1

           1       2

           0      1

121  in base 3 = 16

121 is missing number

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