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Topic: Mysterious 45
Message: Posted by: SteveFowkes (Aug 22, 2005 03:33PM)
There are two puzzles based on the number 45. The first is fairly easy but the second requires a bit more lateral thinking.

1. You can divide 45 into 4 parts so that if you add 2 to one, subtract 2 from another, multiply another by 2 and divide the last by 2, the result from each calculation will be equal. How is it so divided?

2. Subtract 45 from 45 to leave 45.

Good luck,
Steve
Message: Posted by: NCR (Aug 22, 2005 03:50PM)
1. 8,12,5,20
2. I have no idea.
Message: Posted by: SteveFowkes (Aug 23, 2005 05:17AM)
Correct on the first but like I said, the second one requires lateral thinking.
Message: Posted by: TomasB (Aug 23, 2005 01:10PM)
If you have 45 coins (five 10-cents and 40 1-cent) and remove 45 cents you have 45 cents left.

/Tomas
Message: Posted by: SteveFowkes (Aug 23, 2005 07:17PM)
Tomas,

I like your answer. It's not the one I was thinking of but I can't fault it. My way is a lot more devious though, and a little abstract.

Perhaps I should re-phrase the question to 'name two ways of subtracting 45 from 45 to leave 45'

Steve
Message: Posted by: Sapient (Aug 23, 2005 11:51PM)
If I write "45-45" it could be interpreted as meaning a number between 45 and 45, which is kind of 45, but that is stupid. I wish I hadn't typed that. I really wish I hadn't submitted this reply.
Message: Posted by: SteveFowkes (Aug 24, 2005 02:19AM)
Sapient,
And here I was thinking that you were the King of lateral thinking!! Only joking.

Clue. There is an actual subtraction involved but that's just a piece of the puzzle. Tomas was sort of getting there-ish but in a different way.

Hope it confuses, I mean helps,

Steve
Message: Posted by: 2hot (Aug 24, 2005 04:43AM)
Hey how do you do the first one I tried all these simultaneous equations but I cant get it
Message: Posted by: TomasB (Aug 24, 2005 05:56AM)
2hot,

8+2=12-2=5*2=20/2 while 8+12+5+20=45 as NCR wrote in the second post in this thread.

Glad to hear that my answers wasn't what you were looking for on the second question. Got quite happy when I came up with that solution. ;) Does the "real" answer has anything to do with digging or emtying something then leaving a pile or space of 45?

/Tomas
Message: Posted by: leonard (Aug 24, 2005 07:54AM)
How about:

45 written in base 6 = 113 less
45 written in base 7 = 63 equals
45 written in base 9 = 50 .
Message: Posted by: SteveFowkes (Aug 24, 2005 10:18AM)
Tomas, still only one pat on the back I'm afraid. It has nothing to do with holes. It's purely a number thing. Keep thinking.

Leonard, Oh so close but oh so far. It would make a good puzzle though. 45-45=50.

Another clue. It's sum sum!

Steve
Message: Posted by: NCR (Aug 24, 2005 12:28PM)
Would it be acurate to state that within this puzzle 45 represents the number 45 that we would normally think of, all three times that it is used?
Message: Posted by: SteveFowkes (Aug 24, 2005 03:09PM)
It wouldn't be entirely accurate, no.

A dead giveaway clue. 45 is the sum of the sum.

Steve
Message: Posted by: NCR (Aug 24, 2005 03:48PM)
Even with that clue, I'm still almost completely stumpted. I have some kind of idea in the back of my mind, but I can't quite figure out what it is.
Message: Posted by: Sapient (Aug 25, 2005 10:42AM)
[quote]
On 2005-08-24 11:18, SteveFowkes wrote:
Leonard, Oh so close but oh so far. It would make a good puzzle though. 45-45=50.
[/quote]

Leonard's solution does work, as 50 IS 45 in base 9. It may not be the right solution, but I think it is brilliant.
Message: Posted by: SteveFowkes (Aug 25, 2005 02:02PM)
Yes, you're right Sapient. Leonards solution does indeed work and is very cleverly thought out. Sorry Leonard.

This is now getting a little silly. Name THREE ways to subtract 45 from 45 to get 45!

I think Tomas and Leonard deserve gold stars. My solution though is still out there. To be honest, It's not as clever as the 2 already found but it's my solution and I'm sticking to it!!
Message: Posted by: thefifth (Aug 25, 2005 11:04PM)
I don't think this is what your looking for, but its a shot. (4+5)-4.5=4.5
Message: Posted by: SteveFowkes (Aug 27, 2005 10:26AM)
Thefifth, no it's not what I'm looking for but a good try nonetheless.

Regards,
Steve
Message: Posted by: SteveFowkes (Sep 8, 2005 04:17PM)
Finally, the answer - or at least mine anyway.

If you add up the numbers from 1 to 9, the result = 45. So,

9 8 7 6 5 4 3 2 1 = 45, minus
1 2 3 4 5 6 7 8 9 = 45
_________________
8 6 4 1 9 7 5 3 2 = 45

Once again, hats off to Tomas and especially Leonard for their solutions.

Kindest regards,
Steve