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**Piggin_Scooter****Member**- Registered: 2005-10-17
- Posts: 3

I enjoy playing puzzle donkey & i'm a bit late getting around to PD4. So I have no-one around on the usual forums to help. PD4 2.11 is a mth puzzle & I believe the minus signs are used to create a ^ symbol. However I do not know how this symbol works.

The puzzle is below :-

Puzzle 11: Calc-mule-ations

PuzzleDonkey had been given a new set of fridge magnets for his birthday.

He wasn't very excited, though - there was a rather limited range of options.

His set comprised seven of each of the following symbols:

1 + - (

He decided that he'd try and arrange them on his fridge so that they gave the highest possible number.

Of course, it would be cheating if he were to simply combine digits to make larger numbers such as 111 - the largest individual number he'd use was one. He tried rotating a minus to look like a one, too, but that looked well dodgy so he decided against it.

After a week or so, he got bored of the arrangement of magnets on his fridge, so decided to take the equation down. Much to his dismay, a pair of the bracket magnets fell into his carrot dicer and were discombobulated beyond repair.

He presently got his kit out again and aimed to make an equation with the pieces he had left that'd yield the smallest possible positive result.

He wasn't the best at mental arithmetic, so rounded off the outcome to the latter equation to five decimal places, then got out a pen and paper and multiplied this approximation by the larger number he'd generated earlier.

What was the outcome to this little sum?

Please can you give me some hints on what to do & explain the use of the ^ symbol??

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**Zach****Member**- Registered: 2005-03-23
- Posts: 2,075

The ^ symbol is the same as raising to the power of. For example; 2^2 is 4. 2^3 is 8. 2^4 is 16. So on and so forth.

I bet you didn't know it, but I'm a fiddle player too.

And if you'd care to take a dare, I'll make a bet with you.

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

The largest number is, I think, (1+1)^((1+1)^(1+1+1)) = 2^(2^3) = 2^8 = 256.

The smallest is, I think, (1+1)^(-(1+1)^(1+1+1)) = 2^(-2^3) = 2^-8 = 1/256.

Multiplying these together gives 1. But there are probably better numbers than that and so that's probably not right.

Why did the vector cross the road?

It wanted to be normal.

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**Zach****Member**- Registered: 2005-03-23
- Posts: 2,075

Wow. I got that.

I bet you didn't know it, but I'm a fiddle player too.

And if you'd care to take a dare, I'll make a bet with you.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,529

Gee, I am still confused. What about the limited supply of "(" ?

Did I misread it, or were there only 7, and for second equation only 5?

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**Piggin_Scooter****Member**- Registered: 2005-10-17
- Posts: 3

Thanks a lot guys, you have allowed me to get to the correct answer, however I'm still confused on how the smallest number is obtained with two brackets less. I wonder if the fact they were crushed in the carrot dicer made them turn into { } ??

By the way, anyone who fancy's some mental challenges try www.puzzledonkey.com & see how far you can get! I'm now on puzzle 32 of the 4th puzzle donkey.

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

I gave it a go, but I'm stuck on puzzle 1.

Why did the vector cross the road?

It wanted to be normal.

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**ryos****Member**- Registered: 2005-08-04
- Posts: 394

I got stuck on puzzle 3. I tried averaging the colors (based on individual squares), and it came out purple, but that didn't work...That's a tough one.

El que pega primero pega dos veces.

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**Piggin_Scooter****Member**- Registered: 2005-10-17
- Posts: 3

The first one is a typical example of the trickiness of the donkey. "Starts with A" describes the answer however the answer does not begin with a letter A. "Looking up skirts" is the main clue but get your mind away from internet sleeze & think about alternative meanings for looking up rather than literally turning your head skyward.

The third one requires breaking out from the puzzle different base colours. You will need to use some spectrum knowledge to understand how colours are made & therefore if they overlap they would make an alternative colour. There are only three main colours each one leads you to a letter, these then make up the answer.

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**Zach****Member**- Registered: 2005-03-23
- Posts: 2,075

My answer's for the first one would've worked.

I got it in the end.

I bet you didn't know it, but I'm a fiddle player too.

And if you'd care to take a dare, I'll make a bet with you.

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