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# Find smallest function for 24 permutations

## Question

Guest

You have few calculator functions:

- : 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

## 2 answers to this question

• 0
bonanova    76

Cute puzzle. I think I have the idea.

Here's a start, more to come after I get some zzzzzzzzzzz's.

----------------------------------------------------------

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

----------------------------------------------------------

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Guest

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.

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