Using only the numbers 3, 3, 3 and 3 once and + - * / once find 7?

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Discussion Overview

The discussion revolves around a mathematical puzzle that challenges participants to use the numbers 3, 3, 3, and 3 exactly once along with the arithmetic operations +, -, *, and / each exactly once to arrive at the number 7. The scope includes combinatorial reasoning and exploration of potential solutions.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant suggests the expression 3 + 3 + 3/3 = 7 as a potential solution.
  • Another participant argues that this solution uses the + operator twice, which contradicts the problem's requirements.
  • A participant discusses the combinatorial aspect of the problem, noting that there are 24 possible combinations of operators but emphasizes the need to use each operator only once.
  • Some participants express doubt about the feasibility of the problem, questioning whether it is indeed possible to achieve the target number with the given constraints.
  • One participant points out that any combination of operations will yield multiples of 3, suggesting that reaching 7 may not be possible without additional numbers or operations.
  • There is a mention of a similar problem involving five 3's that can yield 7, but this also raises the issue of using operators multiple times.
  • Another participant highlights the ambiguity regarding the use of parentheses in the problem, which could affect the outcome.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether the problem is solvable under the given constraints. There are multiple competing views regarding the validity of proposed solutions and the interpretation of the problem's requirements.

Contextual Notes

There is uncertainty regarding the use of parentheses in the operations, and participants note that the problem may require more than four instances of the number 3 to achieve the desired result.

Natasha1
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Hi,

At the end of our lecture today, the lecturer gave us this simple yet impossible puzzle.

My friend and I have tried to find the answer but in vain...

Using only the numbers 3, 3, 3 and 3 once and using only the four arithmetic + - * / once can you make the number 7.

The closest I have got is 6 or 8 but not 7.

3*3 all / 3 and then + 3 = 6
or
3*3 then - 3/3 = 8

How to find 7?? Is this actually possible?
 
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3 + 3 + 3/3 = 7
 
think of it in terms of combinatorics with the operators:

3 op1 3 op2 3 op3 3

so there's 4 choices for the first, 3 for the third, 2 for the last one = 24 choices

Phyzguy's solution is almost correct except that he repeated the + operator and the problem says to use each operation once.

3+3-3*3=-3
3+3-3/3=5
3+3*3-3=9
3+3*3/3=6
3+3/3-3=1
3+3/3*3=3.33333

3-3+3*3=9
3-3+3/3=1
3-3*3-3=-9
3-3*3/3=0
3-3/3+3=5
3-3/3*3

...
 
Can't do 3 + 3 + 3/3 = 7 as you are using + twice
 
Are you saying it's therefore impossible?
 
Natasha1 said:
Are you saying it's therefore impossible?

I can't tell you the answer only how to think about the problem as it was assigned by your prof.
 
Pity.
 
Natasha1 said:
Pity.

You can't finish the other 12 choices to complete the proof?
 
are you sure the prof or you have the correct problem?
a classic is using 5 "3" and all the operators

(3*3 + 3)/3 + 3 = 7
 
  • #10
But then you are using + twice too
 
  • #11
3 and 7 are prime numbers. Any combination of operations you try (except for 3/3) will be a multiple of 3. If you use 3/3 = 1, then you'd have to add or subtract the 3/3 to something else, since multiplying would result in a multiple of 3 again, and dividing would result in a fraction.

The problem doesn't state if you're allowed to use parenthesis to group operations.

If you're suppose to used + - * / excactly one, that's four operators, so you'd need five 3's.
 

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