- #31
- 19,859
- 10,849
Opening this back up because we still need 89, 91,93!
Challenge Challenge where you have to make each number from four 4s
- Thread starter Joffe
- Start date
-
- Tags
- Challenge
Click For Summary
SUMMARY
The forum discussion revolves around the challenge of creating each integer from 1 to 100 using exactly four instances of the number 4 and various mathematical operations. Participants share numerous solutions, including factorials, square roots, and decimals, while debating the rules regarding the use of certain operations. Notably, solutions for numbers such as 33 and 93 are highlighted, with participants seeking simpler expressions and discussing the validity of using square roots and logarithms.
PREREQUISITES- Understanding of basic arithmetic operations (addition, subtraction, multiplication, division)
- Familiarity with factorial notation (n!)
- Knowledge of square roots and their properties
- Concept of repeating decimals and their representation
- Explore advanced mathematical operations such as logarithms and their applications
- Research combinatorial mathematics and its relation to number formation challenges
- Learn about mathematical proofs and simplifications for complex expressions
- Investigate the use of factorials in combinatorial problems and their implications
Mathematics enthusiasts, puzzle solvers, educators looking for engaging challenges, and anyone interested in exploring creative mathematical expressions using limited resources.
- #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
- 4,166
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!
Similar threads
- · Replies 2 ·
- · Replies 1 ·
- · Replies 18 ·
- · Replies 12 ·
Comp Sci
Trapezoidal rule for a set of data
- · Replies 6 ·
- · Replies 6 ·
- · Replies 11 ·
- · Replies 10 ·
- · Replies 3 ·