Math Is Fun Forum

Josh

Member

Registered: 2006-06-14

Posts: 1

5 Tough Puzzles

I have 5 tough puzzles that I've been trying to crack for ages and just can't get the answers, so I'd really appreciate it if someone could help me out. Thanks, Josh.

Number seqeunce 1:

Here's a number sequence:
1, 11, 21, 1211, 111221, 312211...
Find the rule and post the two next numbers in the sequence.

Number seqeunce 2:

Here's a number sequence:
111, 112, 21123, 1312, 2114, 121, 25262, 73123...
Find the rule and post the two next numbers in the sequence.

Number seqeunce 3:

Here's a number sequence:
101010, 1120, 222, 132, 110, ...
Find the rule and post the two next numbers in the sequence.

Number seqeunce 4:

What numbers should be put instead of question marks:
4, 7, 6, 2, 3, 7, 2, ?, ?.

Two Integers:

I'm thinking of two integer numbers, each if them is more than 1 and their sum is less than 100.
I tell my friend Serge the sum of these two numbers, and another friend, Polly, product of these two numbers.
Then such a dialog took place:
P: I can't determine what are these numbers.
S: Ah, i knew you wouldn't be able to do this.
P: Oh, then i know what they are!
S: Oh, then i know them too!

Can you determine the numbers?

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: 5 Tough Puzzles

The last seems like a variation of: Two Consecutive Numbers

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: 5 Tough Puzzles

For #1, say each digit out loud:

1: one
11: one one
21: two one(s)
1211: one two, one one

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

raju

Member

Registered: 2011-02-08

Posts: 1

Re: 5 Tough Puzzles

for the given puzzle the order would be
1, 11, 21, 1211, 111221, 312211...

followed by
13112221
1113213211