Brain Exercise...

[Sparkle]

Go me!

Not sure. I'll post one soon. Just haven't because I am still waiting for this baby to come. She has given me two false alarms and I am now over due. I get induced Wensday if she doesn't come by then.

[SekoETC]

Oh, remember to post pictures after she'd born.

[Sparkle]

Alright. Will do.

[Misato]

For the sake of my boredom...I always enjoy this one.

1
11
21
1211
111221
312211
13112221

What 2 rows of numbers comes next in this series?

[Peter]

For the sake of my boredom...I always enjoy this one.

1
11
21
1211
111221
312211
13112221

What 2 rows of numbers comes next in this series?

It would be kind of annoying to post the answer, so I won't.

[joo]

For the sake of my boredom...I always enjoy this one.

1
11
21
1211
111221
312211
13112221

What 2 rows of numbers comes next in this series?

Ahahahahah! That's brilliant.

[joo]

How about this one, then.

What is the least number of weights that can be used on a set of scales to weigh any whole number of kilograms from 1 to 40, and what are the values of the weights?

[EchoMan]

6: 1, 2, 4, 8, 16, 32 ?

[gejyspa]

I know the answer, Misato, so I won't give it.. but here's one I gave my kids.. it took them FOREVER, with lots of hints, to get it.. what numbers come next in this sequence:
3, 3, 5, 4, 4, 3, 5, 5, 4, _, _, _ ?

[Peter]

Yes, your solution is right, although there are more possible solutions.
1,2,4,8,16 + my guess is anything between 9 and 32 is correct

[Peter]

I know the answer, Misato, so I won't give it.. but here's one I gave my kids.. it took them FOREVER, with lots of hints, to get it.. what numbers come next in this sequence:
3, 3, 5, 4, 4, 3, 5, 5, 4, _, _, _ ?

(1) 3,3;(2) 5;(3) 4,4;(4) 3;(5) 5,5;(6) 4 I made groups of (a) number(s) here split by ";". Any group of (a) number(s) is changed three groups later, the double become solo and the solo becomes double. Group 1 (3,3) is later in group 4 (3). Group 2 (5) becomes (5,5) in group 5.
Group 7 should be the alternate for group 4 (3,3)
Group 8 should be the alternate for group 5 (5)
This would mean 3,3,5

[gejyspa]

I know the answer, Misato, so I won't give it.. but here's one I gave my kids.. it took them FOREVER, with lots of hints, to get it.. what numbers come next in this sequence:
3, 3, 5, 4, 4, 3, 5, 5, 4, _, _, _ ?

(1) 3,3;(2) 5;(3) 4,4;(4) 3;(5) 5,5;(6) 4 I made groups of (a) number(s) here split by ";". Any group of (a) number(s) is changed three groups later, the double become solo and the solo becomes double. Group 1 (3,3) is later in group 4 (3). Group 2 (5) becomes (5,5) in group 5.
Group 7 should be the alternate for group 4 (3,3)
Group 8 should be the alternate for group 5 (5)
This would mean 3,3,5

You would think, but no.... and in fact, I will GIVE you next three, and ask you for the three after that:
3, 3, 5, 4, 4, 3, 5, 5, 4, 3, 6, 6, _, _, _

[Peter]

You would think, but no.... and in fact, I will GIVE you next three, and ask you for the three after that:
3, 3, 5, 4, 4, 3, 5, 5, 4, 3, 6, 6, _, _, _

Maybe it's not the solution you were looking for, but my solution is perfectly valid. That said... I cheated and find it brilliant.

[gejyspa]

But essentially, you are using one cycles (of 3 groups) and using that as a basis for you solution. There are infinite solutions that just use one cycle. For example, I could have argued, with similar reasoning to yours, that it should be 6,6,3, because the pairs go up by one each time, and singletons cycle through 3,5,4,3,5,4. There isn't enough basis for you to make that claim, because your groups are too big to be meaningful...

[Peter]

But essentially, you are using one cycles (of 3 groups) and using that as a basis for you solution. There are infinite solutions that just use one cycle. For example, I could have argued, with similar reasoning to yours, that it should be 6,6,3, because the pairs go up by one each time, and singletons cycle through 3,5,4,3,5,4. There isn't enough basis for you to make that claim, because your groups are too big to be meaningful...

Ofcourse I do not agree

In this explanation you cannot tell if 354 is the full cycle. It might be 3546 or 35462. One can't tell. In my explanation there is actually a full circle of the "rules".

Again I love the original and I would have never found it.