Unutterably Silly Quiz

[pdurrant]

Are the numbers all years in the 20th century?
1901, 1903, 1922, 1966, 1970, 1981?

In which case, there's something that happened in each of those years, but I've no idea what!

Originally Posted by SneakySnake

something to do with square roots? hmmmmmmmm brain hurting...

I don't know how to do it backwards...

You are on to something.

Originally Posted by pdurrant

Are the numbers all years in the 20th century?
1901, 1903, 1922, 1966, 1970, 1981?

In which case, there's something that happened in each of those years, but I've no idea what!

No, nothing like that.


I promised a big new clue so here it is. The first three terms of a linked series:

1,4,36,?

[Daithi]

Is the next number in your linked series 256 or 324?

No and no.

Here is expansion of clues, including extending original series one element further:

Original series:

1,3,22,66,70,81,94,?

Linked series:

1,4,36,144,144,121,144,?

[Bilbo1967]

Originally Posted by Hamlet53

No and no.

Here is expansion of clues, including extending original series one element further:

Original series:

1,3,22,66,70,81,94,?

Linked series:

1,4,36,144,144,121,144,?

Hmmm...this may as well be in Chinese a far as I'm concerned

[Daithi]

Well, I can see that the linked series is made of squares, but I still don't see the pattern

1,4,36,144,144,121,144,?

1, 2, 6, 12, 12, 11, 12

[issybird]

Originally Posted by Daithi

Well, I can see that the linked series is made of squares, but I still don't see the pattern

1,4,36,144,144,121,144,?

1, 2, 6, 12, 12, 11, 12

I was getting a pretty pattern:

1², 1² X 2², 2² X 3², 3² X 4²....

but then I ran out of steam

[pdurrant]

I'm stumped.

[SneakySnake]

It is something to do with the factors and squares. Brain really hurting now. We need a mathematician.

The sequence makes sense using that, but I can't make it go any further.

[Bookpossum]

I count (sorry) myself lucky if I can get the cheque book balance right. But I enjoy watching the rest of you wrestle with it!

Well since SneakySnake and pdurrant have both had the opportunity to respond after the additional clues I will now provide the answer. I admit this was probably a difficult one, especially if one did not see the pattern of connection in the first few series elements. SneakySnake was certainly on the correct path though.

The only thing immediately obvious about the second related series is those numbers were indeed all squares. The means of generation of the first series was that all those numbers, starting with one, have the property that all divisors (including 1 and the number itself) when summed yield a square. Examples are probably the clear way to illustrate:

1 divisors {1} sum of divisors 1 = 1^2 (the trivial case)
3 divisors {1,3} sum of divisors 4 = 2^2
22 divisors {1,2,11,22} sum of divisors 36 = 6^2
66 divisors {1,2,3,6,11,22,33,66} sum of divisors 144 = 12^2
70 divisors {1,2,5,7,10,14,35,70} sum of divisors 144 = 12^2
81 divisors {1,3,9,27,81} sum of divisors 121 = 11^2
94 divisors {1,2,47,94} sum of divisors 144 = 12^2

The next number with this property is 115 that curiously also yields 144 or 12^2; {1,5,23,115}. The number after that is 170; {1,2, 5,10,17,34,85,170}; 324 = 18^2. That is as far as I computed.

So anyway Stitchawl furnished the correct answer to one of the three parts of my puzzle and so he is up next. I wonder what math puzzler he will provide?

[Bookpossum]

He'll probably give us one about motorbikes!

[Stitchawl]

Originally Posted by Hamlet53

Examples are probably the clear way to illustrate:.................
The next number with this property is 115 that curiously also yields 144 or 12^2; {1,5,23,115}. The number after that is 170; {1,2, 5,10,17,34,85,170}; 324 = 18^2. That is as far as I computed.

Now why didn't I think of that!?!
Bill Cosby: "Hey Dad!! One and One is Two!! Isn't that something! One and One is Two!! Dad?... what's a Two?"

Originally Posted by Bookpossum

He'll probably give us one about motorbikes!

Well, since you suggested it... About a bike maker, but not about bikes!
Everyone all over the world is familiar with the name 'Harley Davidson.' And although I ride a Yamaha cruiser, virtually every older Japanese who walks past me as I'm putting on my helmet in a parking lot asks; "Harury desuka?" (is it a Harley ?)

So I'll ask you:
Although most famous for its motorcycles, bikes are just a small part of the manufacturing production of this company.

1) During W.W. II, Harley turned the majority of its production facilities to what war need? (Non-motorcyle. Though H-D did make 90,000 military bikes, they made a LOT more of this need)

2) After the war ended, and until the real boom in bikes began (in the early '80's,) the company's major money-maker was What Product?


Should you be caught or captured, the Secretary will disavow all knowledge of this mission.


Stitchawl

[SneakySnake]

1 - did they make tanks?
2 - Wanky T-shirts?

[issybird]

2. Lawn mowers?