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Little Maths Puzzler

Orson

Well-known Member
I know you folks like a challenge, but this is one my daughter asked me yesterday - her maths teacher had set it and we're stuck :)

Make the numbers 1 to 20 using four lots of 4 (so 4, 4, 4, 4) in any combination, and any mathematical symbol. S you can use 44, 4 to the power of 4, and so on.

for example

to make 6 we have ((4 + 4) / 4) + 4 = 6

to make 15 we have (44 / 4) + 4 = 15

to make 10 we have (44 - 4) /4 = 10

and so on.

But we're stuck on 19 :confused:

Any ideas.
 

Liquid101

Distinguished Member
(44/4) + (4+4) = 19

EDIT:

I was wrong - I missed this bit.

Make the numbers 1 to 20 using four lots of 4 (so 4, 4, 4, 4) in any combination, and any mathematical symbol. S you can use 44, 4 to the power of 4, and so on.

Doh!
 
Last edited:

Orson

Well-known Member
Thanks to all, I think KrisLee seems to have it. But I have to confess to having to look up what the '!' meant in mathematical terms :blush: Never come accross that one before. (that I remember anyway)

What level are we talking here? :)
She's 6...











:devil:
..teen
 

Singh400

Distinguished Member
I've definitely come across the function "!" but I couldn't remember what it did, so I too had to look it up. Props to KrisLee for getting the right answer :smashin:
 

imightbewrong

Distinguished Member
I've definitely come across the function "!" but I couldn't remember what it did, so I too had to look it up. Props to KrisLee for getting the right answer :smashin:

Indeed.

Factorial comes up quite a lot - e.g. in working out combinations: How many ways are there of arranging four people on a bench? A. 4! = 4x3x2 = 24. 10 people = 10! = 3.6 million ish - it grows pretty quickly :)
 

DPinBucks

Distinguished Member
Following on from that, what's the largest number you can make from four 4s?

I think it's 4!^(4!^44!), but I don't know how to prove it. The numbers are too large for Excel.
 

Iccz

Distinguished Member
Following on from that, what's the largest number you can make from four 4s?

I think it's 4!^(4!^44!), but I don't know how to prove it. The numbers are too large for Excel.

We're gonna need a bigger calculator :(

Could you not add another ! after the brackets? 4!^(4!^44!)!, or am I in need of more caffeine?
 

Liquid101

Distinguished Member
Completely unrelated, but nevertheless tenuously linked.

My mother's birthdate could be expressed as 4/4/44 and I was born on her birthday :)
 

GasDad

Remembered (1964-2012)
We're gonna need a bigger calculator :(

Could you not add another ! after the brackets? 4!^(4!^44!)!, or am I in need of more caffeine?

Wolfram Gives the answer as a factor of 10^10^10

4!^(4!^44!) = 10^(10^(10^54.56454490771793)) (link)

4!^4!^4!^4!= 10^(10^(10^33.26501536145719)) (link)

Taking Iccz's we get

4!^(4!^44!)! = 10^(10^(10^(10^54.56454490771793)))

But of course you can stick brackets around that and get:

(4!^(4!^44!)!)!= 10^(10^(10^(10^(10^54.56454490771793))))

Obviously at this point we realise we can carry on adding parenthesis and plings - so to infinity and beyond
 
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Singh400

Distinguished Member
Following on from that, what's the largest number you can make from four 4s?

I think it's 4!^(4!^44!), but I don't know how to prove it. The numbers are too large for Excel.
Yeah Excel 2003 won't do it. Maybe I can crash Excel 2010 beta at home? :D

Code:
[SIZE="3"]24^(24^2658271574788450000000000000000000000000000000000000000)[/SIZE]

Is what the calculation is.
 

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