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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,
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.

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

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'

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)
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,

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)

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?

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!

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.

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)
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.

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.

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,