Five three

sahithmukku

New member
Joined
Aug 25, 2012
Messages
1
I have been working on a summer packet for math and i have come to two math problems i cannot solve.
They are both very similar. You have to use five threes to make a number. For example, to make 21 the equation would be (33-3)-(3x3).
You have to use five threes in any way possible to get the number.
So my question is, how do you use five three's to make 44 and 51?
 
Hello, sahithmukku!

How do you use five 3's to make 44 and 51?

\(\displaystyle 44 \;=\;33 + \dfrac{33}{3}\)

\(\displaystyle 51 \:=\:3^3 + 3^3 - 3\)


By the way: .\(\displaystyle 37 \:=\:\frac{333}{3\times3}\)
 
Last edited:
You have to use five threes to make a number.
For example, to make 21 the > > > equation would be (33-3)-(3x3). < < <

You have to use five threes in any way possible to get the number.
I don't know which ways you were/are allowed. You should state them.

For example:

\(\displaystyle +, \ \ -, \ \ \times, \ \ \div, \ \ /, \ \ fraction \ \ bar, \ \ exponents, \ \ bracketing \ \ symbols \ \ such \ \ as \ \ ( \ ), \ \ etc. \)

Edit: And concatenation? For example, placing the digit 3 next to a digit 3 to make the number 33.



Edit:

sahithmukku,

I apologize for not catching that you stated "equation" for the above, but that is incorrect.
It is an expression. However, 21 = (33 - 3) - (3 x 3) is an equation.
 
Last edited:
They are both very similar. You have to use five threes to make a number.
For example, to make 21 the equation would be (33-3)-(3x3).

You have to use five threes in any way possible to get the number.

So my question is, how do you use five three's to make 44 and 51?

May you use the factorial sign and/or the decimal point?


44 = 3(3)(3!) - 3/.3

44 = 3!/.3 + (3 + 3/3)!

44 = (3!)(3!) + 3! + 3!/3 . . . . . Edit: This was added in today.



51 = 3(3)(3 + 3) - 3 . . . . . no factorial sign and no decimal point

51 = 33 + 3! + 3! + 3!

51 = 3(3! + 33/3)

51 = 3(3(3!) - 3/3)

51 = 3(3!) + 3^3 + 3!

51 = 3(3! + 3! + 3!) - 3
 
Last edited:
Any chance that you might also have a solution for the results 50 and/or 59?
Same rules as above, use 5 threes etc.
 
Any chance that you might also have a solution for the results 50 and/or 59?
Same rules as above, use 5 threes etc.

Which rules? Several possible operations have been suggested; do you have any restrictions?

Square root? Greatest integer function? Decimals? Factorials? ...
 
Sorry, I thought that was clear from the previous answers given....


+, −, ×, ÷, /, fraction bar, exponents, bracketing symbols such as ( ), factorial sign, square root, decimals only if you wouldn't have to leave out a zero, (i.e. NO .3, but 3.3 yes), and concatenation
 
Sorry, I thought that was clear from the previous answers given....

+, −, ×, ÷, /, fraction bar, exponents, bracketing symbols such as ( ), factorial sign, square root, decimals only if you wouldn't have to leave out a zero, (i.e. NO .3, but 3.3 yes), and concatenation
No, the OP never replied about what the rules were; and since you're a different person from a different context, who knows what rules (if any) you might have. There are many variations. (I have never heard of rejecting .3, which is perfectly valid mathematically.)

My thought for 50 was (3*3+3+3)/.3 .

But the way I generally solve these is to generate a lot of possible expressions and write them all next to their values, then try to vary each type to fill in gaps. It's hard to aim at a specific value. There is software (probably websites) that can do this for you, if the goal is just to get an answer.
 
Top