2 replies to this topic

[Benson]

You have few calculator functions:
+ : add
- : subtract
* : mutiply
/ : divide
% : get remainders from divide
** : power

Notation:
1.f(x) = {1,2,3,4} means f(1)=1, f(2)=2, f(3)=3, f(4)=4.
2.cost = 1 means the function uses one operator.

So, please find all 24 functions of 4! with minimum of operations. That is,
f1(x)={1,2,3,4} f1(x)=x (cost = 0)
f2(x)={1,2,4,3} f2(x)=?
f3(x)={1,3,2,4} f3(x)=?
f4(x)={1,3,4,2} f4(x)=?
f5(x)={1,4,2,3} f5(x)=?
f6(x)={1,4,3,2} f6(x)=?
f7(x)={2,1,3,4} f7(x)=?
f8(x)={2,1,4,3} f8(x)=?
f9(x)={2,3,1,4} f9(x)=?
f10(x)={2,3,4,1} f10(x)=?
f11(x)={2,4,1,3} f11(x)=?
f12(x)={2,4,3,1} f12(x)=?
f13(x)={3,1,2,4} f13(x)=?
f14(x)={3,1,4,2} f14(x)=?
f15(x)={3,2,1,4} f15(x)=?
f16(x)={3,2,4,1} f16(x)=?
f17(x)={3,4,1,2} f17(x)=?
f18(x)={3,4,2,1} f18(x)=?
f19(x)={4,1,2,3} f19(x)=?
f20(x)={4,1,3,2} f20(x)=?
f21(x)={4,2,1,3} f21(x)=?
f22(x)={4,2,3,1} f22(x)=?
f23(x)={4,3,1,2} f23(x)=?
f24(x)={4,3,2,1} f24(x)=5-x (cost = 1)

Note:
1.it does not allow recursive function calls.
2.power operator costs 2 and others cost 1.
*3.divide operator gets the floor of the divide result. that is, 3/2 => 1

[bonanova]

Cute puzzle. I think I have the idea.
Here's a start, more to come after I get some zzzzzzzzzzz's.

Spoiler for ...

----------------------------------------------------------
f1(x)={1,2,3,4} f1(x)= x cost = 0
f2(x)={1,2,4,3} f2(x)=?
f3(x)={1,3,2,4} f3(x)=?
f4(x)={1,3,4,2} f4(x)=?
f5(x)={1,4,2,3} f5(x)=?
f6(x)={1,4,3,2} f6(x)=? 4-(x+2)%4 cost=3
----------------------------------------------------------
f7(x)={2,1,3,4} f7(x)=?
f8(x)={2,1,4,3} f8(x)=? 4-(x+1)%4 cost=3
f9(x)={2,3,1,4} f9(x)=?
f10(x)={2,3,4,1} f10(x)=? 1+x%4 cost=2
f11(x)={2,4,1,3} f11(x)=?
f12(x)={2,4,3,1} f12(x)=?
----------------------------------------------------------
f13(x)={3,1,2,4} f13(x)=?
f14(x)={3,1,4,2} f14(x)=?
f15(x)={3,2,1,4} f15(x)=? 4-x%4 cost=2
f16(x)={3,2,4,1} f16(x)=?
f17(x)={3,4,1,2} f17(x)=? 1+(x+2)%4 cost=3
f18(x)={3,4,2,1} f18(x)=?
----------------------------------------------------------
f19(x)={4,1,2,3} f19(x)=? 1+(x+2)%4 cost=3
f20(x)={4,1,3,2} f20(x)=?
f21(x)={4,2,1,3} f21(x)=?
f22(x)={4,2,3,1} f22(x)=?
f23(x)={4,3,1,2} f23(x)=?
f24(x)={4,3,2,1} f24(x)= 5-x cost = 1
----------------------------------------------------------

[Benson]

Great~ You solve the first 6 via "shift" and "make circle" them. You still need to use "*" or "/" to
"expand" and "compress" the distance for others.