All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Numbers > Sequences
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)

Comments: ( Back to comment list | You must be logged in to post comments.)
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
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (1)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (6)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information