- #31
- 19,879
- 10,886
Opening this back up because we still need 89, 91,93!
Challenge where you have to make each number from four 4s
- Context: Challenge
- Thread starter Joffe
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Discussion Overview
The discussion revolves around a challenge to create each integer from 1 to 100 using exactly four instances of the number 4, employing various mathematical operations. Participants share their solutions, propose alternative methods, and clarify the rules regarding permissible operations.
Discussion Character
- Exploratory
- Mathematical reasoning
- Debate/contested
Main Points Raised
- Some participants present solutions for numbers 1 to 100 using four 4s, employing operations like addition, subtraction, multiplication, division, factorials, and decimals.
- There is a discussion on the inclusion of square roots, with some arguing against it as it introduces the number 2, while others suggest it could be allowed.
- Some participants propose using repeating decimals and logarithmic functions, while others challenge the validity of these methods.
- Several participants express preferences for certain operations over others, indicating a desire to maintain the challenge's difficulty.
- Corrections and refinements to previously suggested solutions are made, with participants acknowledging errors and suggesting improvements.
- New solutions are proposed for numbers that remain unsolved, with some participants expressing excitement over creative approaches.
Areas of Agreement / Disagreement
Participants generally do not reach consensus on the inclusion of certain mathematical operations, such as square roots and logarithms. There are multiple competing views on what constitutes a valid solution, and the discussion remains unresolved regarding the strict rules of the challenge.
Contextual Notes
Some participants express limitations on the use of specific mathematical symbols and operations, leading to a variety of interpretations of the challenge's rules. The discussion reflects a range of assumptions about what is permissible in constructing solutions.
Who May Find This Useful
Individuals interested in recreational mathematics, puzzle-solving, or mathematical creativity may find this discussion engaging and informative.
- #32
cmb
- 1,128
- 128
What are the rules? What is wrong with the 93 above using sqrt and ! .Greg Bernhardt said:
Is % allowed?
- #33
cmb
- 1,128
- 128
I am thinking about the 'rules' and I think 0.4 is a cheat.
It implies 10. The decimalised column is 'Base 10' and infers a number which is only the value '0.4' by virtue of the assumption the base is 10 and thus the decimal column is worth "10^-1".
If you work in the bizarre base of 'Base 1/22.5' (i.e. the number "10" = 2/45ths (denary)) rather than 'Base 10' you can ALSO include a reference to the required base value using a '4'.
.4 + (4/4) (Base { 0.0\bar{4}})
and
.4 - (4/4) (Base { 0.0\bar{4}})
I am not using zeros any more than '.4' implies base 10, so the solution above should be no more nor less 'allowed' than .4 .
Thoughts?
It implies 10. The decimalised column is 'Base 10' and infers a number which is only the value '0.4' by virtue of the assumption the base is 10 and thus the decimal column is worth "10^-1".
If you work in the bizarre base of 'Base 1/22.5' (i.e. the number "10" = 2/45ths (denary)) rather than 'Base 10' you can ALSO include a reference to the required base value using a '4'.
.4 + (4/4) (Base { 0.0\bar{4}})
and
.4 - (4/4) (Base { 0.0\bar{4}})
I am not using zeros any more than '.4' implies base 10, so the solution above should be no more nor less 'allowed' than .4 .
Thoughts?
- #34
dextercioby
Science Advisor
- 13,404
- 4,184
93 can be done.
## 93 = 4 \cdot 4! - \frac{4!}{4!} ##
## 93 = 4 \cdot 4! - \frac{4!}{4!} ##
- #35
fbs7
- 345
- 37
-- "Mathematician #1, what's the Meaning of Life, Power of Love and The Purpose of Man?"
-- "These are non-mathematical thingies! The answer is ∞/∞!"
-- "Mathematician #2, what's Our Place In Universe, The Truth of All and The Reason Of Everything?"
-- "These are non-mathematical thingies! The answer if 0/0!"
-- "Mathematician #3, say you have five 3... what can... "
-- "AHH! Gimme-gimme-gimme! I can make 173 with that! And 81! And 33.3333!
-- "I can make 128! Hey, don't touch my 3!"
-- "Step aside! I can make 0! Hahaha! Take That!"... "No, my 17 is better! You'll get a 3 in your nose!"... "Open way! I can make 3.14159!"... "Ya'll don't think big enough - I can make 357 trillion! Brlrlrlrlr!"... "Hey!"
That's a madhouse
!
-- "These are non-mathematical thingies! The answer is ∞/∞!"
-- "Mathematician #2, what's Our Place In Universe, The Truth of All and The Reason Of Everything?"
-- "These are non-mathematical thingies! The answer if 0/0!"
-- "Mathematician #3, say you have five 3... what can... "
-- "AHH! Gimme-gimme-gimme! I can make 173 with that! And 81! And 33.3333!
-- "I can make 128! Hey, don't touch my 3!"
-- "Step aside! I can make 0! Hahaha! Take That!"... "No, my 17 is better! You'll get a 3 in your nose!"... "Open way! I can make 3.14159!"... "Ya'll don't think big enough - I can make 357 trillion! Brlrlrlrlr!"... "Hey!"
That's a madhouse
!
Last edited:
- #36
cmb
- 1,128
- 128
Let ! be the operator such that x! = 89.x/(4+4+4+4)
Therefore
89 = (4+4+4+4)!
When we apply arbitrary rules to what mathematics "means" and when an answer is "right" or "wrong", then it isn't really mathematics any more, it is more like politics or accountancy!
Therefore
89 = (4+4+4+4)!
When we apply arbitrary rules to what mathematics "means" and when an answer is "right" or "wrong", then it isn't really mathematics any more, it is more like politics or accountancy!
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