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Lowest & Highest (Posted on 2005-02-24) Difficulty: 3 of 5
What are the next two numbers in these two related sequences?

1 , 4 , 3 , 11 , 15 , 13 , 17 , --- , ---
10 , 9 , 60 , 90 , 70 , 66 , 69 , --- , ---

See The Solution Submitted by Syzygy    
Rating: 3.3333 (3 votes)

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Solution Solution To The First Part | Comment 9 of 11 |
(In reply to Answer by K Sengupta)

Let the ith term of the given sequence be S(i).

Then, S(i) = smallest positive integer whose spelled out version
contain precisely (i+2) letters.

For example, the first term of the sequence is 1, which is spelled out as "one",which contains 3 letters. Therefore, S(1) = 3.

Similarly, S(2) = 4, since 4 is the smallest positive integer whose spelled out version contain precisely 4 letters.

We now observe that "twenty four" contains 10 letters and checking for the positive integers 1 to 24, we observe that 24 is indeed the smallest number with this property.
Thus, S(8) = 24

Similarly, checking for the numbers 1 to 23, we observe that the
word "twenty three" contains 11 letters, so that 23 is the smallest
positive integer with this property.

Therefore, S(9) = 23

Consequently, the required missing terms are 24 and 23.


  Posted by K Sengupta on 2008-05-27 15:56:33
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