Puzzle of the day

Beja · May 22, 2020

A woman asked how many eggs in her basket? She said:
I don't know but....
If I moved them 2 by 2, or 3 by 3, or 4 by 4, or 5 by 5, or 6 by 6, then there's always 1 left. Only when I move them 7 by 7 is where nothing is left.

How many eggs she had?
Stay @home

aeric · May 22, 2020

My guess is 7^n where n > 0

JordiCP · May 22, 2020

my guess is that the eggs at the bottom will be broken ?
(oops, edited)

301 + n*420, where n>=0

Beja · May 22, 2020

aeric said:
My guess is 7^n where n > 0

Try again.. Try to test for all 7 cases

aeric · May 22, 2020

Beja said:
Try again.. Try to test for all 7 cases

How big is her basket?

Alexander Stolte · May 22, 2020

aeric said:
How big is her basket?

She has a WinRar License

rabbitBUSH · May 22, 2020

You'd need turtle library recursive fractal graphics to work backwards to count the nodes in the guide to the galaxy, so I asked the chickens in the yard : the answer is

42.

Jorge M A · May 23, 2020

I Have 301 Eggs! ?

B4X:

#Region Project Attributes
    #MainFormWidth: 600
    #MainFormHeight: 600
#End Region

Sub Process_Globals
    Private fx As JFX
    Private MainForm As Form
End Sub

Sub AppStart (Form1 As Form, Args() As String)
    MainForm = Form1
    'MainForm.RootPane.LoadLayout("Layout1") 'Load the layout file.
    MainForm.Show
    CalculateEggs
    
End Sub

'Return true to allow the default exceptions handler to handle the uncaught exception.
Sub Application_Error (Error As Exception, StackTrace As String) As Boolean
    Return True
End Sub

Sub CalculateEggs()
    Dim i As Int=7
    
    Do While True
        If 1 = (i Mod 2) And 1 = (i Mod 3) And 1 = (i Mod 4) And 1 = (i Mod 5) And 1 = (i Mod 6) And 0 = ( i Mod 7) Then
            Log($"I Have ${i} Eggs!"$)
            Exit
        End If
        i=i+1
    Loop
End Sub

aeric · May 23, 2020

Jorge M A said:

I Have 301 Eggs! ?

B4X:

#Region Project Attributes
    #MainFormWidth: 600
    #MainFormHeight: 600
#End Region

Sub Process_Globals
    Private fx As JFX
    Private MainForm As Form
End Sub

Sub AppStart (Form1 As Form, Args() As String)
    MainForm = Form1
    'MainForm.RootPane.LoadLayout("Layout1") 'Load the layout file.
    MainForm.Show
    CalculateEggs
    
End Sub

'Return true to allow the default exceptions handler to handle the uncaught exception.
Sub Application_Error (Error As Exception, StackTrace As String) As Boolean
    Return True
End Sub

Sub CalculateEggs()
    Dim i As Int=7
    
    Do While True
        If 1 = (i Mod 2) And 1 = (i Mod 3) And 1 = (i Mod 4) And 1 = (i Mod 5) And 1 = (i Mod 6) And 0 = ( i Mod 7) Then
            Log($"I Have ${i} Eggs!"$)
            Exit
        End If
        i=i+1
    Loop
End Sub

How about other possibilities of value of i greater than 7?

Jorge M A · May 23, 2020

aeric said:
How about other possibilities.

I' don't care. There is only one question in the original puzzle and I found a "method" to resolve it. You can try sending rockets to the moon, but I took it just for fun.

aeric · May 23, 2020

Jorge M A said:
I' don't care. There is only one question in the original puzzle and I found a "method" to resolve it. You can try sending rockets to the moon, but I took it just for fun.

I think @JordiCP 's answer (spoiler) is correct. I don't know how to get that answer.

LucaMs · May 23, 2020

In the meantime, the eggs have "expired", so the woman had to throw them, so the result is: zero.

JordiCP · May 23, 2020

aeric said:
think @JordiCP 's answer (spoiler) is correct. I don't know how to get that answer

Solved it with modular arithmetics.
As I wasn't sure of the result, also made a small B4I program, similar to @Jorge M A to check it.

sorex · May 23, 2020

I think it's 61201 eggs.

(s)he doesn't remove 2 but 2 by 2 so the mod check is different

Jorge M A · May 23, 2020

JordiCP said:
Solved it with modular arithmetics.

? I wonder if it works the same way for avocados instead of eggs...

JordiCP · May 23, 2020

Jorge M A said:
? I wonder if it works the same way for avocados instead of eggs...

Only if they are not too mature, otherwise the woman would be carrying a bag full of guacamole ?

rabbitBUSH · May 23, 2020

Jorge M A said:
I wonder if it works the same way for avocados instead of eggs...

I will ask my neighbour he has 40 000 avocado trees, he should know, then we will know if we should still count the eggs in the basket.

ilan · May 24, 2020

the answer is 120

B4X:

    For i = 2 To 7
        Log(120 Mod i)
    Next

logs:

Waiting for debugger to connect...
Program started.
0
0
0
0
0
1

sorex · May 24, 2020

it's the opposite, ilan.

it should list 1,1,1,1,1,0

ilan · May 24, 2020

sorex said:
it's the opposite, ilan.

it should list 1,1,1,1,1,0

sorry, the answer is 301 (i misread the first post)

B4X:

    Dim n(6) As Int = Array As Int(0,0,0,0,0,0)
    Dim nrstart As Int = 7
    Dim found As Boolean
    Do Until found
        For i = 2 To 7
            n(i-2) = nrstart Mod i
        Next
        If n(0) = 1 And n(1) = n(0) And n(2) = n(0) And n(3) = n(0) And n(4) = n(0) And n(5) = 0 Then
            found = True
            Exit
        End If      
        nrstart = nrstart + 1
    Loop

    Log(nrstart)

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