Create 4 4s to Make 35 37 39 & 41

  • Context: High School 
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Discussion Overview

The discussion revolves around the challenge of creating the numbers 35, 37, 39, and 41 using exactly four instances of the number 4. Participants explore various mathematical operations and representations to achieve these targets, including addition, subtraction, multiplication, division, and the use of factorials and exponents.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • Some participants argue that using only addition, subtraction, multiplication, and division on four 4's cannot yield odd numbers, as all results will be even.
  • One participant suggests using two of the fours to produce one, allowing for combinations like 4 + 4 + 4/4 = 9, but expresses doubt about reaching higher odd numbers than 17.
  • Another participant proposes using the fours as strings, such as 444/4 = 111, and explores the use of factorials, noting that 4! + 4! - 4/4 = 47, which is not a target number.
  • Several participants present near solutions, such as (\frac{4^2}{\sqrt{1/4}}) - 4^0 = 31 and variations that approach the target numbers.
  • One participant successfully finds 44 - 4 - 4^0 = 39 and 44 + 4^0 - 4 = 41, indicating progress towards the challenge.
  • There is discussion about the acceptability of using exponents and roots, with some participants questioning the rules regarding their use in this context.
  • Another participant mentions the fundamental theorem of arithmetic in relation to the nature of numbers, but it is unclear how this relates directly to the challenge.

Areas of Agreement / Disagreement

Participants express differing opinions on the feasibility of achieving the target numbers with the given constraints. There is no consensus on the methods allowed or the validity of certain mathematical operations, leading to multiple competing views.

Contextual Notes

Some participants assume that only basic operations are allowed, while others explore the use of factorials and exponents, leading to potential confusion about the rules governing the challenge.

Joseph
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I need to make 35,37,39,and 41 using four 4's.
 
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If the only operations you can perform on the fours is addition, subtraction, multiplication, and division, then you can't get any of them.

You'll always get an even number, regardless of the operations you use or the order you use them in.

cookiemonster
 
cookiemonster said:
If the only operations you can perform on the fours is addition, subtraction, multiplication, and division, then you can't get any of them.

You'll always get an even number, regardless of the operations you use or the order you use them in.

cookiemonster

No, you can use two of the fours to produce one, as in 4 + 4 + 4/4 = 9. Or 4*4 + 4/4 = 17. Subtracting the quotient gives 7 and 15 respectively.

Offhand, given the four function constraint, I don't see a way to get a higher odd number than 17.

Can we use the four fours as strings instead of individual digits? 444/4 = 111, an odd number. 44/4 + 4 = 15. (44/4)^4 = 14,641, a very big odd number.

On the other hand, can we use factorials? 4! is 24, so 4! + 4! - 4/4 = 47. Drats, it's not on the target list. (4 * 4! - 4) / 4 is 23. Still no go.

Sorry, but I don't see a trick to get the desired numbers. :confused:
 
Last edited:
This is to cheat, but: ((4*4)4)/4=164/4=41
 
Aren't all numbers primes or products of primes?
 
I came pretty close for one of them.

[tex](\frac{4^2}{ \sqrt{1/4}}) - 4^0 = 31[/tex]

Can you see what I did?

Here's another one.

[tex](\frac{4}{ \sqrt{1/4}}) 4 - 4^0 = 31[/tex]

[tex](\frac{4^2}{ \sqrt{1/4}}) + 4^0 = 33[/tex]
 
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Another one.

[tex]44 - 4 - 4^0 = 39[/tex]
 
I got to go, so I'll do the rest when I get back.

Use my tricks and you are good to go.
 
[tex]44 + 4^0 - 4 = 41[/tex]

Got back from lunch. Time to study boring accounting.
 
  • #10
Aha! I forgot to consider 4/4 = 1.

Good point.

cookiemonster
 
  • #11
JasonRox said:
I came pretty close for one of them.

[tex](\frac{4^2}{ \sqrt{1/4}}) - 4^0 = 35[/tex]

Can you see what I did?

Here's another one.

[tex](\frac{4}{ \sqrt{1/4}}) 4 - 4^0 = 31[/tex]

[tex](\frac{4^2}{ \sqrt{1/4}}) + 4^0 = 37[/tex]

I'd presumed that using other numerals like 2 and 0 for exponents wouldn't be allowed. At least that's the case in problems of this sort I've seen before. Non-numeric mathematic symbols like square root are OK, but a cube root isn't be, since you have to use a numeral to specify it. If you can use a 4^2 to mean squared, why can't you say 4*5 or anything else?
 
Last edited:
  • #12
I put squared to make it easier. If you count again, you will see there is four.

Remember all numbers have exponent 1's.

If I'm allowed square roots, I did nothing wrong. Square root is the same as exponent 1/2.

I didn't break any rules if you allow 1/2.

I believe that you are restricted to the number one. If you add 1/2 and 1/2 you get 1, and since you allowed 1/2, I can manipulate it to do other things. Here is how it works:

-1/2-1/2=-1 (I used 1/4 instead of 4^-1, because it didn't work for some reason)
1/2-1/2=0
1/2+1/2=1 (The regular exponent.)

See I broke no rules. :)
 
  • #13
More...

[tex]4! + 4^2 + 4^0 = 41[/tex]

There is 4 Four's.
 
  • #14
Let's here the opposite of Fermat's Last Theorem!

[tex]x^n + y^n = z^n[/tex], is possible in infinite amounts for n<2.
 
  • #15
Was this a class assignment? If so, let me know if changing a four to a one by raising it to the zeroth power is acceptable. I'd be surprised, but I'd like to know.

Also, earlier you wrote:

JasonRox said:
Aren't all numbers primes or products of primes?

All natural numbers are, that is, positive integers. Obviously negative numbers and fractional numbers aren't.

Further, each natural number is either prime or the product of primes in a unique way. There is one and only one such representation for each. That's the fundamental theorem of arithmetic.
 

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