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Four generations (Posted on 2020-07-06) Difficulty: 3 of 5
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.)
Hints/Tips Where is the KISS solution | Comment 6 of 9 |
I hoped someone will present a simple analytical solution.

2 hints:
1st
S2 contains all 6 digit numbers such that each is a permutation of six successive  digits, like 215364 or 785346.

2nd
Forget 143-it is a red herring.
Show that none of S2 members can be divisible by 11.
It is very easy.

  Posted by Ady TZIDON on 2020-07-06 16:22:46
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