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I have some maths puzzles which I've been trying to figure out for ages but have not succeeded. I'd really appreciate it if someone could help me out. Thanks, Josh.

Number sequence - 1

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

Number sequence - 2

Another number sequence, totally different rule, and it's tougher than previous.
111, 112, 21123, 1312, 2114, 121, 25262, 73123...
Find the rule and post two next numbers in the sequence.

Number sequence - 3

101010, 1120, 222, 132, 110, ...

One more sequence

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 Josh 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?

Good luck, Josh.

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Question

Number sequence - 1

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

Solution
Solution: It's actually quite simple :) After starting the sequence with 1, each term in the sequence consists of groups of two numbers based on the previous term - the first being the quantity and the second specifying which digit.

Example: the first term is 1, which has "one 1" in it, therefore 11.
11 has "two 1's" in it, therefore 21.
21 has "one 2 and one 1" in it and therefore 1211.

Question
Number sequence - 3

101010, 1120, 222, 132, 110, ...

Soltuion

101010, 1120, 222, 132, 110, 60, 52, 46, 42, 39, 36, 33, 30

a(n) = 18 written in the base n

Question
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 Josh 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?

Solution
http://www.mathematik.uni-bielefeld.de/~sillke/PUZZLES/logic_sum_product

Rashakil fol, feel free to do the others yup :-) ...

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I have a book of puzzles which I've being doing like since forever but these are the only one's which I can't do. I'd just like to finally get the answers :cheesy: Iamthwee, I just have a question. In the link for the two intergers their range is from 1 -20. Does it matter that the question I asked has a range from 1 - 100, would the answer still be the same?

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101010, 1120, 222, 132, 110, 60, 52, 46, 42, 39, 36, 33, 30

a (n) = 18 written in the base n

What number is written on base n? I figured out the answer to my intergers question. Thanks.

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