What is the number?
If you divide the number by 2 there will remainder of 1.
If you divide the number by 3 there will remainder of 1.
If you divide the number by 4 there will remainder of 1.
If you divide the number by 5 there will remainder of 1.
If you divide the number by 6 there will remainder of 1.
If you divide the number by 7 there will remainder of 1.
If you divide the number by 8 there will remainder of 1.
If you divide the number by 9 there will remainder of 1.
If you divide the number by 10 there will remainder of 1.
If you divide the Number by 11 there will remainder of 0.
If you divide the number by 3 there will remainder of 1.
If you divide the number by 4 there will remainder of 1.
If you divide the number by 5 there will remainder of 1.
If you divide the number by 6 there will remainder of 1.
If you divide the number by 7 there will remainder of 1.
If you divide the number by 8 there will remainder of 1.
If you divide the number by 9 there will remainder of 1.
If you divide the number by 10 there will remainder of 1.
If you divide the Number by 11 there will remainder of 0.
posted by Ragknot at
10:56 PM
15 Comments:
This post has been removed by the author.
is it 34560?
James,
No, it is not 34560
34560 / 2 has a remainder of zero.
The correct number would have a remainder of 1.
10! (= 3,628,800) is divisible by all numbers 2 to 10.
So 10! + 1 (= 3,628,801) gives a remainder of 1 in each case.
It also happens to be divisible by 11.
There may be smaller numbers which also fit the requirements but I haven't checked.
Tle lowest common multiple of 2,3,...,10 is 2520. So 2520 has
remainder 0 after dividing by 2,3,...,10. So 2520x+1 has remainder
1 after dividing by 2,3,...,10. But 2520 mod 11 = 1.
We want n = 2520x + 1 = 0 (mod 11) => n = x + 1 = 0 (mod 11)
=> x = 10 and n = 25201.
I saw 36 numbers less than one million that works to fit this.
Chris found the first of the 36!!
Wiz found the 131st number that fits.
In my previous (which was for the smallest positive integer that does
the job), you can add multiples of 11 to x =>
2520(10+11y)+1 = 25201 + 27720y for y = 0,1,2... all do the job.
This post has been removed by the author.
Yup, 25,201.
This post has been removed by the author.
Sub test2()
While i < 200
n = n + 11
For m = 2 To 11
____j = n Mod m
____If m = 11 And j = 0 Then
________i = i + 1: Debug.Print i, n
____Else
________If j <> 1 Then Exit For
____End If
Next m
Wend
End Sub
is it?
3628801?
10!+1=3628801
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