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.
Answers
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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