perplexus.info :: Numbers : Four generations

Four generations (Posted on 2020-07-06)

Let S be a set of all six-digit integers.

Let S1 be a subset of S, including all members of S such that each consists
of distinct digits.
Let S2 be a subset of S1, including all members of S1 each with 5 being the difference between its largest digit and its lowest one.
Let S3 be a subset of S2, comprising all elements of S2 divisible by 143.

What is the cardinality of S3 ?

Explain your way of reasoning.

No Solution Yet Submitted by Ady TZIDON

Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

apologies to steven

| Comment 4 of 9 |

(In reply to re: part 1 via computer by Charlie)

I neglected to check for duplicate digits.

Corrected section of code:

If highest - lowest = 5 Then

good = 1

For i = 2 To Len(ns)

If InStr(ns, Mid(ns, i, 1)) < i Then good = 0

If good Then ct = ct + 1: lastmemb = n: Text1.Text = Text1.Text & n & " "

End If

DoEvents

with this it finds no solutions so the cardinality is zero.

Posted by Charlie on 2020-07-06 10:34:16

Please log in:

Login:
Password:
Remember me:

Sign up! \| Forgot password

Search:

Search body:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (7)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info