The Four 4's Game

[Nervous Rex]

38 = 4! + !4 + !4 - 4

 

[Crossbreed]

39 = !4 x 4 + (Γ(4)/√4)

(See Wikipedia article)

 

[Jeremiah]

40 = (4 * 4 + 4) * √4

 

[Nervous Rex]

41 = 4 * !4 + !4 - 4

 

[Crossbreed]

42 = !4 x 4 + 4 + √4

 

[Nervous Rex]

43 = Γ(4)! / (4 * 4) - √4

 

[FreeDiver]

44 = 44 + 4 - 4

 

[Crossbreed]

45 = !4 x (4 + 4/4)

 

[Nervous Rex]

46 = 4! + 4! - 4/√4

 

[FreeDiver]

47 = 4! + 4! - 4/4

 

[Crossbreed]

48 = 4 x 4 x (Γ(4)/√4)
48 = 4! + 4! + (4 - 4)

 

[Nervous Rex]

48 = 4 x 4 x (Γ(4)/√4)

That one is just plain fun.

 

[Nervous Rex]

49 = (Γ(4) + 4/4)^√4

 

[Crossbreed]

50 = √(4 x 4)/(√4 x 4%)

 

[Nervous Rex]

51 = 4! + !4 + !4 + !4

 

[Nervous Rex]

52 = 4(!4 + √4 + √4)

 

[Crossbreed]

53 = 4! + 4! + √(!4) + √4
54 = (!4 x √4 x √4)/√.(4)

 

[Nervous Rex]

53 = 4! + 4! + √(!4) + √4

√(!4) is a great way to make 3! I could have used it earlier.

I think I need to make a chart of of numbers and ways to make them with 1, 2 and 3 fours. Then, when I try to make some number with 4 fours, I can look up and see if the chart lists two numbers that add up to it, with the correct total number of fours.

E.g. I would have 48 in two fours with 4! + 4! and 48 in 3 fours with √(!4) * 4 * 4.

 

[Nervous Rex]

55 = 44 + !4 + √4
56 = √(4 * 4 * 4)! / Γ(4)!
57 = 44 + !4 + 4

I have all the way up to 82 worked out, but I don't want to spoil the fun.

 

[Crossbreed]

I think I need to make a chart of of numbers and ways to make them with 1, 2 and 3 fours.

I made a similar chart for two 4s. I can do offsets from +0 to 18 (except 14 & 17). I can do bigger ones, too, but there are more "holes" between them, the higher that I go.

Using a base, like (Γ4 x 4) + ?, you can generate any number between 6 & 42, except (7, 10, 38, 41). Using different bases should cover those holes, besides more unique solutions.