Math challenge question

Here is a math challenge question for the forum. If you post an answer, I suggest you hide it behind the spoiler tags.

First, as an illustration, the number 42 can be written as a mathematical expression that uses no digit other than 7 in this way:

.

Consider the number 331,775. Write a mathematical expression, involving any well-known mathematical operators/functions, that is equal to 331,775 and that uses only the digit 2 and no other digits.

The valid answer that uses the digit 2 the fewest times will be considered the winner. There is no prize other than the glory of winning.

Hint: There is at least one relatively simple answer. But the section called Rule Clarifications below attempts to anticipate and answer a number of questions that zealous forumites might ask.


Rule Clarifications
- Specifically, 0 and 1 are forbidden digits, as are 3-9
- Use of the symbol π is not allowed. Explicit use of e as the mathematical constant that is the base of natural logarithms is also not allowed. These are symbols that represent constant irrational numbers and, as such, are not operators or functions
- math symbols for functions/operators that use letters (from any alphabet) are allowed. Sin(2) is an allowable expression, as is ln(2*2) or the zeta function ζ(2).
- spelling out a number, such as ONE or THREE, is not acceptable because these are not mathematical operators or functions, they are alphabetic representations of numbers.

Notes:
This site Math symbols provides the ASCII symbol (in the first column) for mathematical symbols (in the 2nd column). However, this is not a keyboarding contest: if you want to use a math symbol that you can't type in simply with a keyboard, you may simply spell it out in some way in your formula and explain what it is.

Example: "Zeta( )" may be used to represent the well-known zeta function, ζ( ) -just define it as such.

I'm not taking credit, but shortening Romes' answer:

Probably not allowed but yolo....



Edit: fixed small mistake #2

Damn I hate that

Just used it once.

Quote: gordonm888

Consider the number 331,775. Write a mathematical expression, involving any well-known mathematical operators/functions, that is equal to 331,775 and that uses only the digit 2 and no other digits.

Meh, I just won't use the number 2 at all.

Now u really mad.

LOL, I expected many creative answers and the forum did not disappoint.

1. Romes' answer is correct and he figured it out in precisely the way that I had expected.

2. Crystal Math's answer is correct and is written in the form that I had expected or hoped for -and it uses only 6 2s. There is a "less pure" variant of this form that is more efficient because it only uses 5 2s. See the spoiler button on the bottom.


3. RS's answers are very creative and technically valid (except for the last one in which all the terms are not written out, LOL) I had anticipated several ways to write an expression equal to 331,775 without using any digits at all but was not clever enough to write rules to block all the possible ways.

4. Wizard's answer is correct but hardly the most efficient. But his answer was completely orthogonal to any of the approachs that I had thought of - so high marks for originality.

Since we're not giving away any prizes, we can afford to be generous in announcing the winner.

We announce that the Romes-CrystalMath function was the winner.
We expect RS to sue us in Math Court and to eventually win his lawsuit and be declared the winner on a technicality.
The Wizard is awarded the Mr. Congeniality award for his answer.

And here is the "less pure" variant of the Romes-CrystalMath function that uses one less 2.

https://youtu.be/ZYewWA-Zcr4

🤣

Jokes aside, every so often in the puzzle section of the news paper, they ask to make a certain number using only four 4's and any mathematical symbols.

Quote: Ibeatyouraces

https://youtu.be/ZYewWA-Zcr4

🤣

I graciously acknowledge that I am a nerd. I once lost a girlfriend because I rented the Revenge of the Nerds movie (in your post) as the movie we should watch one evening. I was also student body president at Rensselaer Polytechnic Institute at a time that it had a male-to-female ratio of 10:1, so my buddies jokingly referred to me as "King of the Nerds."

Quote: Ibeatyouraces

Jokes aside, every so often in the puzzle section of the news paper, they ask to make a certain number using only four 4's and any mathematical symbols.

Wow. I had no idea. I thought I had invented some new mathematical amusement with this math challenge. Sometimes it seems like everything in 'recreational mathematics' has already been done by someone else.

Quote: gordonm888

I graciously acknowledge that I am a nerd. I once lost a girlfriend because I rented the Revenge of the Nerds movie (in your post) as the movie we should watch one evening. I was also student body president at Rensselaer Polytechnic Institute at a time that it had a male-to-female ratio of 10:1, so my buddies jokingly referred to me as "King of the Nerds."



Wow. I had no idea. I thought I had invented some new mathematical amusement with this math challenge. Sometimes it seems like everything in 'recreational mathematics' has already been done by someone else.

Next time I see one, I'll post it here.

Do answers have to be in base 10? In base 331,774:

22 / 2

Quote: Ace2

Do answers have to be in base 10? In base 331,774:

22 / 2

Correct me if I'm reading this wrong, but isn't 22/2=11?

Quote: Ibeatyouraces

Correct me if I'm reading this wrong, but isn't 22/2=11?

In base 10, 22/2 = 11.

In base 331,774, you have: 22/2

In base 10 that's equivalent to:

((331774^0)*2 + (331774^1)*2) / ((331774^0)*2)


One of my thoughts was to do this in a different base, but was too lazy to do the necessary multiplying and hwatnot.

Quote: RS

In base 10, 22/2 = 11.

In base 331,774, you have: 22/2

In base 10 that's equivalent to:

((331774^0)*2 + (331774^1)*2) / ((331774^0)*2)


One of my thoughts was to do this in a different base, but was too lazy to do the necessary multiplying and hwatnot.

This just proves that answers to these questions are just opinions. Psrsonally to me, these🍎🍎🍎🍎 are grapes.

Quote: Ace2

Do answers have to be in base 10? In base 331,774:

22 / 2

Clever. But you needed to indicate the base/radix and you did that with: "In base 331,774:" which uses forbidden digits.