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.