# four 1's

using four ones what is the maximum number can be obtained(can use any arithmetic operators)

## Replies

11^11 π
• aarthivg
godfather
11^11 π
rite
Few days back CEan-silverscorpion had solved same question in this section only. π
• aarthivg
godfather
Few days back CEan-silverscorpion had solved same question in this section only. π
sorry. i haven't noticed it.
• Kaustubh Katdare
Can we generalize this? The maximum number obtained using any number 'x' using n times?

Like: Max number that can be constructed using 3, 5 times or using 5, 3 times?
• Dancer_Engineer
The_Big_K
Can we generalize this? The maximum number obtained using any number 'x' using n times?

Like: Max number that can be constructed using 3, 5 times or using 5, 3 times?
5 ^ (5 ^ 5) ?
• Kaustubh Katdare
I'm thinking of coming up with a formula.
• Dancer_Engineer
The_Big_K
I'm thinking of coming up with a formula.
Ok. Cool. π

I think the 'raise to' operator gives the Max number in majority cases.

The formula would depend on
i) whether we are using same operator or different operators.
ii) whether we are using the numbers together or individually.
• simplycoder
(1+1)/(1-1) is this valid form, even though division by 0 is meaning less, I would like to frame my solution slightly different manner.

Concept of a division:
If we divide a number x with number y then the quotient we get is inversly proportional to the y(divisor).
Say if we follow, 8/8 will be 1. 8/4 will be 2, 8/2=4 8/1 will be 8 and so on..
Now it can be noted that as the divisor goes on decreasing, the quotient increases.

Mathematically speaking, zero is the smallest possible number where as infinity is the largest possible number. Since this cannot be fixed at any value, it cannot be strictly defined and limited to some number as 1,2,3 and so on.

Various people can assume various values of infinity and thus it is said to largest possible number.(Which is what exactly is asked in the question)

By the concept of division, Largest possible quotient can be accquired by smallest possible divisor, in this case I propose the divisor to be 0.

Well I think this can be a indefinite solution for indefinite question(Question whose goal can interpreted differently).

I think in general mathematics, its meaning less to divide by 0 but question here asked is the largest possible number, so my answer would be infinity,
• Dancer_Engineer
Wow. π

Ok, the question is this:
The maximum number obtained using any number 'x' using n times.

Here we are not finding the maximum number possible.

We have to find maximum number using any number 'x' using n times.

Like the example given by Big K,
Max number that can be constructed using 3, 5 times or using 5, 3 times?

So if we solve to find max number using 5, 3 times;
based on different conditions it would give different solution.

Case 1: using only 1 operator
Sol: 5 ^ (5 ^ 5)

Case 2: using more than 1 operator
Sol: [5! ^ (5! ^ 5!)]!

Case 3: using the numbers individually
Sol: same sol as case 1 and 2

Case 4: using the numbers individually and/or together
Sol: 55! ^ 5! OR 555! OR 5! ^ 55!

Am I making sense hereπ
• sachinswetha
godfather
11^11 π
• sachinswetha
aarthivg
rite
1111!
• ISHAN TOPRE
godfather
Few days back CEan-silverscorpion had solved same question in this section only. π
This is actually one of the puzzles in Shakuntala Devi's book.
• Dancer_Engineer
Someone throw light on my post. π
• Kaustubh Katdare
Okay, I think we need to define the number of operators as well. Else we can repeat the operators a gazillion times and still add a factorial to it to make it even bigger π

I think we should impose a limit of only one operator. Does that make sense? π¨
• Dancer_Engineer
What about the numbers? Do we use the numbers individually / together / both?

You are reading an archived discussion.

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