Brain Exercise...

[gejyspa]

But in the meantime, the correct answer has still not actually been found....
3, 3, 5, 4, 4, 3, 5, 5, 4, 3, 6, 6, _, _, _

[Peter]

I wish everyone good luck, you'll need it with this one *grins*

[joo]

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

No, it's possible to do it with fewer weights than that.

[Peter]

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

No, it's possible to do it with fewer weights than that.

And I thought I had a great solution. It seems I was wrong. I can now do it with 5 weights: 1,2,5,15,25.
When the items weighs 24 kilo, I place the weighs and item like this: item left + 1 kilo and 25 kilo on the right.
34: item left+5+1 and 25+15 right

How am I doing?

[joo]

And I thought I had a great solution. It seems I was wrong. I can now do it with 5 weights: 1,2,5,15,25.
When the items weighs 24 kilo, I place the weighs and item like this: item left + 1 kilo and 25 kilo on the right.
34: item left+5+1 and 25+15 right

How am I doing?

Getting closer. The optimal solution (or the best one I know of) uses one less weight than that.

[Misato]

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, _, _, _ ?

I know the answer to yours, too, but since everyone is refusing to answer mine, I'm not answering yours! *sticks her tongue out*

[joo]

I know the answer to yours, too, but since everyone is refusing to answer mine, I'm not answering yours! *sticks her tongue out*

If you insist on proof of a solution:

http://pastebin.com/xwCAtvPH

[Peter]

starting from 1, they're the number of characters in the spelling of the number.

Since we are spoiling other peoples fun.

[Peter]

1,3,9,27
it took some time, but still

[joo]

starting from 1, they're the number of characters in the spelling of the number.

Since we are spoiling other peoples fun.

...

I posted it as a link for a reason.

1,3,9,27
it took some time, but still

Well done. How did you do it? I was able to work it out algebraically with the knowledge that there were four weights, after realising each one could take a negative value as well.

[Peter]

Well it had to be less numbers than 6 obviously that would mean "negative weights" otherwise you deffinately need 1,2,4,8/7/6/5 to just get to 9. With four numbers the most you would get out of these four is 1+2+4+8=15. That's not even close to 40 but already 4 weights.

So for 8 it must be something like 15-7 or in the correct case 9-1. To get to 40 I needed something like 25 to go with it. That's how I got my first answer with 5 numbers.

Now you said it needed to be less numbers. I was looking for a combination that atleast equals to 40. In my opinion it needed 1 and 3 for the first four numbers. The highest next number to make 5 with is 9. (9-3-1=5) Well, it needs 27 to add up to 40.

[EchoMan]

I never thought of putting weights on "the other side" of the scale too. Devious.

[EchoMan]

Here is one:

In a tennis tournament there are 73 registered participants. If you lose a match you are out. How many games does it take to get the winner of the tournamnet?

Here the method of solution has to be provided too, as there are right and wrong ways to calculate it.

[Peter]

I probably know nothing about tennis, just like any other sport. So excuse me for saying something stupid.

- I assume that every match has a loser
- there is one winner and 72 losers

Conclusion would be 72 matches. Now tell me why I am wrong .

[EchoMan]

I probably know nothing about tennis, just like any other sport. So excuse me for saying something stupid.

- I assume that every match has a loser
- there is one winner and 72 losers

Conclusion would be 72 matches. Now tell me why I am wrong .

That's correct. Most people try a linear approach, and start dividing 73/2 and so on. The correct solution is to turn the question around: How many games does it take to get 72 losers?