What number will extend the following sequence?

**1, 6, 8, 3, 7, ...**

*Crypto hint:* REBMU NTIGI DEERH TASTI

(In reply to

Answer by K Sengupta)

Reading the crypro hint backwards, and allowing for due punctuation, we obtain:

"It's a three digit number". So, the next number must contain three digits.

We now express each of the given numbers in words, and note the last letter as follows:

Number Expressed in Words Last letter

1 ONE E

6 SIX X

8 EIGHT T

3 THREE E

7 SEVEN N

The last letters in the above table describe the string 'EXTEN'.

We note that the problem title contain the word "EXTEND", and accordingly the last letter of the spelled out version of the next number is D.

Thje smallest number satisfying this condition is 100, since the last letter of "HUNDRED" is D and the last letter of the spelled out version of none of the numbers less than hundred is D.

Consequently, the required next number is D.

*Edited on ***July 28, 2008, 1:11 pm**