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Code: Select all

; Note: the original puzzle provides 12 statements and starts with
; "Given the following twelve statements...", so the first statement
; should ignore the F[1] flag and always be true (see "( N == 1 )").

S := 12 ; number of statements
Output := ""
Loop, % 2**S {
    ;;If !Mod(A_Index,100) ;; optional 'if' to show the loop progress
    ;;    ToolTip, Index: %A_Index%
    SetFlags(A_Index-1), Current := "", Count := 0
    Loop, %S%
        R := TestStatement(A_Index), Current .= R, Count += (R == F[%A_Index%])
    If ( Count >= S-1 )
        Output .= "`n[" Count "] -> " Current
}
ToolTip
MsgBox, % SubStr(Output,2)
Return

;-------------------------------------------------------------------------------------

SetFlags(D) {
    Global
    Local I
    Loop, %S%
        I := S-A_Index+1 , F[%I%] := (D >> (S-A_Index)) & 1
}

;-------------------------------------------------------------------------------------

TestStatement(N) {
    Global
    Local I, C := 0
    If ( N == 1 ) ; This is a numbered list of twelve statements.
        Return ( S == 12 ) ; should always be true
    If ( N == 2 ) { ; Exactly 3 of the last 6 statements are true.
        Loop, 6
            I := S-A_Index+1 , C += F[%I%]
        Return ( C == 3 )
    }
    If ( N == 3 ) { ; Exactly 2 of the even-numbered statements are true.
        Loop, %S%
            C += ( !Mod(A_Index,2) & F[%A_Index%] )
        Return ( C == 2 )
    }
    If ( N == 4 ) ; If statement 5 is true, then statements 6 and 7 are both true.
        Return ( F[5] ? F[6] & F[7] : 1 )
    If ( N == 5 ) { ; The 3 preceding statements are all false.
        Loop, 3
            I := N-A_Index , C += F[%I%]
        Return ( C == 0 )
    }
    If ( N == 6 ) { ; Exactly 4 of the odd-numbered statements are true.
        Loop, %S%
            C += ( !!Mod(A_Index,2) & F[%A_Index%] )
        Return ( C == 4 )
    }
    If ( N == 7 ) ; Either statement 2 or 3 is true, but not both.
        Return ( F[2] ^ F[3] )
    If ( N == 8 ) ; If statement 7 is true, then 5 and 6 are both true.
        Return ( F[7] ? F[5] & F[6] : 1 )
    If ( N == 9 ) { ; Exactly 3 of the first 6 statements are true.
        Loop, 6
            C += F[%A_Index%]
        Return ( C == 3 )
    }
    If ( N == 10 ) ; The next two statements are both true.
        Return ( F[11] & F[12] )
    If ( N == 11 ) ; Exactly 1 of statements 7, 8 and 9 are true
        Return ( F[7]+F[8]+F[9] == 1 )
    If ( N == 12 ) { ; Exactly 4 of the preceding statements are true
        Loop, % N-1
            C += F[%A_Index%]
        Return ( C == 4 )
    }
}

Code: Select all

global S
S := {1: 1}
Recurse(2)
ExitApp

Check2() {
	return (S[2] = (S[7]+S[8]+S[9]+S[10]+S[11]+S[12] = 3))
}

Check3() {
	return (S[3] = (S[2]+S[4]+S[6]+S[8]+S[10]+S[12] = 2))
}

Check4() {
	if (S[5])
		return (S[4] = (S[6]+S[7] = 2))
	else
		return (S[4] = 1)
}

Check5() {
	return (S[5] = (S[2]+S[3]+S[4] = 0))
}

Check6() {
	return (S[6] = (S[1]+S[3]+S[5]+S[7]+S[9]+S[11] = 4))
}

Check7() {
	return (S[7] = (S[2]+S[3] = 1))
}

Check8() {
	if (S[7])
		return (S[8] = (S[5]+S[6] = 2))
	else
		return 
}

Check9() {
	return (S[9] = (S[1]+S[2]+S[3]+S[4]+S[5]+S[6] = 3))
}

Check10() {
	return (S[10] = (S[11]+S[12] = 2))
}

Check11() {
	return (S[11] = (S[7]+S[8]+S[9] = 1))
}

Check12(t=0) {
	Loop 11
		if (S[A_Index])
			t++
	return (S[12] = (t = 4))
}

Check() {
	if (Check2() && Check3() && Check4() && Check5() && Check6() Check7() && Check8() && Check9() && Check10() && Check11() && Check12()) {
		for k, v in S
			if (v)
				Out .= k " "
		MsgBox, % "True statements: " Out
	}
}

Recurse(k) {
	if (k = 13)
		Check()
	else {
		S[k] := 0
		Recurse(k+1)
		S[k] := 1
		Recurse(k+1)
	}
}

Code: Select all

/*
Fib(x) {
    t := -1
    If ( x >= 0 )
        GoSub, Fib_Label
    Else
        MsgBox, Oops!
    Return t
    Fib_Label:
        i := 0, j := 1
        Loop, % x-1
            t := i+j, i := j, j := t
    Return
}

MsgBox, % "Calling Fib(5) ..."
MsgBox, % "Result: " Fib(5)
MsgBox, % "Calling Fib(-3) ..."
MsgBox, % "Result: " Fib(-3)
ListVars
MsgBox, % "ListVars shows the variables are not global."
;GoSub, Fib_Label ; <--- this yields an error
*/

Code: Select all

m := 1, k := 1
loop, 100{
	gosub, label
	MsgBox  % !mod((sqrt(k)), 1 ) ? k " Open" . "`nFactors-" . list . "`nOdd number of factors" : k " Closed " . "`nFactors-" . list . "`nEven number of factors"
	list := "", 	m := 1, k := k + 1
}  
 exitapp
 esc::exitapp
  label:
 loop, % k/2{
  list .= !mod(k, m) ? m "," : ""
   m++
}
list := list . k
return
   

Code: Select all

#SingleInstance, Force
#NoEnv
SetBatchLines, -1

C1 := 0xff0000aa, C2 := 0xff00aa00, C3 := 0xffaa0000

; Uncomment if Gdip.ahk is not in your standard library
;#Include, Gdip.ahk

If !pToken := Gdip_Startup()
{
   MsgBox, 48, gdiplus error!, Gdiplus failed to start. Please ensure you have gdiplus on your system
   ExitApp
}
OnExit, Exit

Width := A_ScreenWidth, WC := Width//2 , Height := A_ScreenHeight, HC := Height//2
	, TopLeftX := (A_ScreenWidth - Width)//2, TopLeftY := (A_ScreenHeight - Height)//2

Gui, 1: -Caption +E0x80000 +LastFound +AlwaysOnTop +ToolWindow +OwnDialogs
Gui, 1: Show, NA

hwnd1 := WinExist(), hbm := CreateDIBSection(Width, Height), hdc := CreateCompatibleDC()
	, obm := SelectObject(hdc, hbm), G := Gdip_GraphicsFromHDC(hdc), Gdip_SetSmoothingMode(G, 4)
	, speed := 1, s := 120, d := 20, h := 120, 2h := h + h

Loop {
	mcx := (mc := Cos(a := Mod(A_Index, 90)* 0.01745329252)) * s
		, mcy := mc * d
		, msx := (ms := Sin(a)) * s
		, msy := ms * d
	
	; Points
	x1 := WC - mcx,  y1 := HC - msy - h
		, x2  := WC + msx, y2 := HC - mcy - h
		, x3  := WC + mcx, y3 := HC + msy - h
		, x4  := WC - msx, y4 := HC + mcy - h
		, yb1 := y1 + 2h, yb2 := y2 + 2h
		, yb3 := y3 + 2h, yb4 := y4 + 2h
	
	; Fill Top
	P1 := x1 "," y1 "|" x2 "," y2 "|" x3 "," y3 "|" x4 "," y4
		, DrawFace(P1, C3, G)
	
	; Fill Vertical Faces
	P1 := x1 "," y1 "|" x4 "," y4 "|" x4 "," yb4 "|" x1 "," yb1
		, P2 := x4 "," y4 "|" x3 "," y3 "|" x3 "," yb3 "|" x4 "," yb4
		, P3 := x2 "," y2 "|" x2 "," yb2 "|" x3 "," yb3 "|" x3 "," y3
		, i :=Mod(A_Index, 360)
	if (i < 90 || (i < 270 && i >= 180))
		DrawFace(x1 < x4 ? P1 : P3, C1, G)
			, DrawFace(P2, C2, G)
	else {
		if (x1 < x4) 
			DrawFace(P1, C2, G)
				, DrawFace(P2, C1, G)
		else 
			DrawFace(P2, C1, G)
				, DrawFace(P3, C2, G)
	}

	UpdateLayeredWindow(hwnd1, hdc, TopLeftX, TopLeftY, Width, Height)
	if (!Mod(A_Index, speed))
		Sleep, 30
	Gdip_GraphicsClear(G)
}

DrawFace(Points, Color, G) {
	pBrush := Gdip_BrushCreateSolid(Color)
		, Gdip_FillPolygon(G, pBrush, Points, 1)
		, Gdip_DeleteBrush(pBrush)
	return
}

p::Pause

Right::
s++
Set_TT("s", s)
return

Left::
s--
Set_TT("s", s)
return

Up::
d++
Set_TT("d", d)
return

Down::
if (d > 0)
	d--
Set_TT("d", d)
return

PGUP::
h++
2h := h + h
Set_TT("h", h)
return

PGDN::
if (h > 0)
	h--
2h := h + h
Set_TT("h", h)
return

Home::
If (Speed < 3)
	Speed++
Set_TT("Speed", Speed)
return

End::
If (Speed > 1)
	Speed--
Set_TT("Speed", Speed)
return

Set_TT(s, v) {
	ToolTip, % s ": " v
	SetTimer, TT, -1500
	return
}

TT:
ToolTip
return

Esc::
Exit:
SelectObject(hdc, obm), DeleteObject(hbm), DeleteDC(hdc)
	, Gdip_DeleteGraphics(G), Gdip_Shutdown(pToken)
ExitApp
Return