Use exactly four 4's to form every integer from 0 to 50

[lookagain]

No, no, no, no trig functions!
What is this baker's dozen all about?

In your thread post, you needed to spell out what "usual operators" means.

As far as I know they would be:

Addition
Subtraction & the negation sign
Division
Multiplication
Exponentiation
Parentheses
Square roots
Concatenation of digits
Decimal points
Regular factorial (no double factorial, etc.)

 

[Steven G]

In your thread post, you needed to spell out what "usual operators" means.

As far as I know they would be:

Addition
Subtraction & the negation sign
Division
Multiplication
Exponentiation
Parentheses
Square roots
Concatenation of digits
Decimal points
Regular factorial (no double factorial, etc.)

And these are the usual one that have been used in the past. To Denis: note there is no trig functions

 

[Denis]

And these are the usual one that have been used in the past. To Denis: note there is no trig functions

Where does it say that in your initial post?

 

[Steven G]

Where does it say that in your initial post?

Have you used trig functs in other similar problems? (knowing you, you probably have). Besides, I like the trig result, I just have to break your balls.

 

[Denis]

Have you used trig functs in other similar problems? (knowing you, you probably have). Besides, I like the trig result, I just have to break your balls.

Outch!!
You allowed Harry's F(n) = nth Fibonacci number, so looked to me like
everything including the kitchen sink was allowed.

 

[Steven G]

Outch!!
You allowed Harry's F(n) = nth Fibonacci number, so looked to me like
everything including the kitchen sink was allowed.

Harry is a very nice person. That's all I'll say.

 

[lookagain]

Harry is a very nice person. That's all I'll say.

Seriously speaking, the Fibonacci function would not be used.

Also, Jomo, your example of 4/4! - 4/4! would not be used as a solution, because it works without
the presence of factorial signs.

* * Edit * * Go to Math is Fun under Four Fours Puzzle. They have all of the
solutions worked out for 0 to 50, and they don't even use any exponentiation.
I don't know what that site meant by the "square function," but ignore it.

 

[Steven G]

Seriously speaking, the Fibonacci function would not be used.

Also, Jomo, your example of 4/4! - 4/4! would not be used as a solution, because it works without
the presence of factorial signs.

I agree about the Fibonacci function not being allowed. I am a bit confused why you say my example is not good. Is the rule that you need to use the simplest expression (ie whatever form you use it must be simple as in no factorials unless they are 100% necessary?)

 

[lookagain]

I am a bit confused why you say my example is not good. Is the rule that you need to use the simplest expression (ie whatever form you use it must be simple as in no factorials unless they are 100% necessary?)

Just as there are primitive (or reduced) Pythagorean triples for right triangles, there are
primitive solutions for these "use numbers/digits and operators to form target number"
puzzles.

There is a uniqueness to 4/4 - 4/4 = 0 with its minimal characters within its context.
Otherwise, you have redundancies of 4/4! - 4/4! = 4!/4 - 4!/4 = 4!/4! - 4!/4! = 4/(4!)! - 4/(4!)! = ...

 

[Denis]

Thanks lookagain; here tizz:

Use exactly four 4's to form every integer from 0 to 50,
using only the operators +, -, x, /, () (brackets), sqrt and ! (factorial).

0 = 44-44
1 = 44/44
2 = 4/4+4/4
3 = (4+4+4)/4
4 = 4*(4-4)+4
5 = (4*4+4)/4
6 = 4*.4+4.4
7 = 44/4-4
8 = 4+4.4-.4
9 = 4/4+4+4
10 = 44/4.4
11 = 4/.4+4/4
12 = (44+4)/4
13 = 4!-44/4
14 = 4*(4-.4)-.4
15 = 44/4+4
16 = .4*(44-4)
17 = 4/4+4*4
18 = 44*.4+.4
19 = 4!-4-4/4
20 = 4*(4/4+4)
21 = (4.4+4)/.4
22 = 44*sqrt(4)/4
23 = (4*4!-4)/4
24 = 4*4+4+4
25 = (4*4!+4)/4
26 = 4/.4+4*4
27 = 4-4/4+4!
28 = 44-4*4
29 = 4/.4/.4+4
30 = (4+4+4)/.4
31 = (4!+4)/4+4!
32 = 4*4+4*4
33 = (4-.4)/.4+4!
34 = 44-4/.4
35 = 44/4+4!
36 = 44-4-4
37 = (sqrt(4)+4!)/sqrt(4)+4!
38 = 44-4!/4
39 = (4*4-.4)/.4
40 = 44-sqrt(4*4)
41 = (sqrt(4)+4!)/.4-4!
42 = sqrt(4)+44-4
43 = 44-4/4
44 = 44.4-.4
45 = 4/4+44
46 = 44-sqrt(4)+4
47 = 4!+4!-4/4
48 = 4*(4+4+4)
49 = (4!-4.4)/.4
50 = 4!/4+44

 

[Steven G]

Thanks lookagain; here tizz:

Use exactly four 4's to form every integer from 0 to 50,
using only the operators +, -, x, /, () (brackets), sqrt and ! (factorial).

0 = 44-44
1 = 44/44
2 = 4/4+4/4
3 = (4+4+4)/4
4 = 4*(4-4)+4
5 = (4*4+4)/4
6 = 4*.4+4.4
7 = 44/4-4
8 = 4+4.4-.4
9 = 4/4+4+4
10 = 44/4.4
11 = 4/.4+4/4
12 = (44+4)/4
13 = 4!-44/4
14 = 4*(4-.4)-.4
15 = 44/4+4
16 = .4*(44-4)
17 = 4/4+4*4
18 = 44*.4+.4
19 = 4!-4-4/4
20 = 4*(4/4+4)
21 = (4.4+4)/.4
22 = 44*sqrt(4)/4
23 = (4*4!-4)/4
24 = 4*4+4+4
25 = (4*4!+4)/4
26 = 4/.4+4*4
27 = 4-4/4+4!
28 = 44-4*4
29 = 4/.4/.4+4
30 = (4+4+4)/.4
31 = (4!+4)/4+4!
32 = 4*4+4*4
33 = (4-.4)/.4+4!
34 = 44-4/.4
35 = 44/4+4!
36 = 44-4-4
37 = (sqrt(4)+4!)/sqrt(4)+4!
38 = 44-4!/4
39 = (4*4-.4)/.4
40 = 44-sqrt(4*4)
41 = (sqrt(4)+4!)/.4-4!
42 = sqrt(4)+44-4
43 = 44-4/4
44 = 44.4-.4
45 = 4/4+44
46 = 44-sqrt(4)+4
47 = 4!+4!-4/4
48 = 4*(4+4+4)
49 = (4!-4.4)/.4
50 = 4!/4+44

Denis, your assignment for the week was to practice your three times table but instead you chose to learn how to copy and paste. I worry about you.

 

[Denis]

Ahhh geezzz Jomo, I did that just for you...
knowing you still don't know how to use google...

 

[Steven G]

Ahhh geezzz Jomo, I did that just for you...
knowing you still don't know how to use google...

You are on a teaching forum. You should show me how to use google instead of googling for me.

 

[JeffM]

Denis, your assignment for the week was to practice your three times table but instead you chose to learn how to copy and paste. I worry about you.

We all do.

 

[Harry_the_cat]

Harry is a very nice person. That's all I'll say.

Nawwww! Thanks Jomo! Take that, Denis!

 

[Harry_the_cat]

And these are the usual one that have been used in the past. To Denis: note there is no trig functions

The problem with

31: ASIN(√4 / 4) + 4/4​

is that ASIN (0.5) = 30 degrees, not just 30. You can't add 30 degrees ​to 1.

 

[Harry_the_cat]

Seriously speaking, the Fibonacci function would not be used.

Also, Jomo, your example of 4/4! - 4/4! would not be used as a solution, because it works without
the presence of factorial signs.

* * Edit * *

Go to Math is Fun under Four Fours Puzzle.​

They have all of the
solutions worked out for 0 to 50, and they don't even use any exponentiation.
I don't know what that site meant by the "square function," but ignore it.

I agree, the Fibonacci number is stretching the friendship.

​

Go to Math is Fun under Four Fours Puzzle​

Isn't that cheating??

 

[Denis]

Seriously, I have a hard time understanding why ! (factorial)
is usually included, but not T(n) (triangular number).
5! = 5*4*3*2*1
T(5) = 5+4+3+2+1

T(5) sure looks more natural to me.

Wonder why a symbol like 5# was never introduced to represent
addition, similarly to 5! representing multiplication.

 

[Harry_the_cat]

Seriously, I have a hard time understanding why ! (factorial)
is usually included, but not T(n) (triangular number).
5! = 5*4*3*2*1
T(5) = 5+4+3+2+1

T(5) sure looks more natural to me.

Wonder why a symbol like 5# was never introduced to represent
addition, similarly to 5! representing multiplication.

Good point. Maybe it will catch on.

 

[Denis]

Ya. Jomo would sure appreciate this, since he finally learned how to add;
sadly, he can't use ! yet, as he's now learning how to multiply