Thanks to all for the discussion and interesting solutions. In our local newspaper there is a math riddle column
coming up with some brainteaser every weekend. The 42 is special since it is mentioned e.g. here:
https://www.scientificamerican.com/article/for-math-fans-a-hitchhikers-guide-to-the-number-42/
I have no idea about the 80. all which comes to mind is, that the column width of punched cards was 80 :)
--
Christoph

In article <t9rhlk$2uh87$1@dont-email.me>,
Gerry Jackson <do-not-use@swldwa.uk> wrote:
>On 03/07/2022 08:26, kuku@physik.rwth-aachen.de wrote:
>> Alexander Wegel schrieb am Samstag, 2. Juli 2022 um 19:18:21 UTC+2:
>>> Alexander Wegel <awe...@arcor.de> wrote:
>>>
>>>> The thing to take home: a schnapszahl is a multiple of 11 in the current
>>>> number base.
>>> Anyway, it's just the same principle as in zbigs code 8-)
>>
>> Alexander, thanks for the "multiple of 11" remark, but doesn't help in
>the problem solution.
>> One could extend the rule to 111 for 3 digit results and so on.
>>
>> @Zbig: the problem to solve is: name all bases in which the given
>number (80,42) is a repdigit number.
>> For the 80, the result should be:
>>
>> 80
>> base number
>> 3 2222
>> 9 22
>
>22 in base 9 is decimal 20
>
>> 19 44
>> 39 22
>> 79 11
>>
>> Your algorithm finds the 9 (only)
>>
>>
>> 42
>> base number
>> 4 222
>> 13 33
>> 20 22
>> 41 11: divisor ( #digits -- n-ones ) 0 tuck ?do base @ * 1+ loop ;
>
>\ Extending Alexander Wegel's idea to 11...1, in bases 2 to 36 ANS max
>\ base
>
>: #digits ( ud -- #digs ) <# #s #> nip ;
>
>: repdigit? ( ud -- f )
> 2dup #digits dup 2 < if drop nip exit then
> divisor sm/rem drop 0=
>;
>
>: report ( n f -- )
> 0= if drop exit then
> base @ >r decimal cr ." Base: " r@ 2 .r
> ." , Number: #" dup 0 .r
> r> base ! ." , Repdigit: " .
>;
>
>: repdigit ( n -- )
> dup 0 ( -- n ud )
> 37 2
> do
> i base ! 2>r
> 2r@ repdigit? ( -- n f )
> over swap report 2r> ( -- n ud )
> loop 2drop drop decimal
>;
>
>#42 repdigit cr
>Base: 4, Number: #42, Repdigit: 222
>Base: 13, Number: #42, Repdigit: 33
>Base: 20, Number: #42, Repdigit: 22 ok
>
>#80 repdigit
>Base: 3, Number: #80, Repdigit: 2222
>Base: 9, Number: #80, Repdigit: 88
>Base: 15, Number: #80, Repdigit: 55
>Base: 19, Number: #80, Repdigit: 44 ok

A better algorithm is this for every BASE and number:

1. BASE > number , trivially true
2. n' = base + 1
3. temp= n' * base + 1
If temp > number, goto 4
set n' to temp, and goto 2
4. if n' divides number, number is repdigit
terminate
>
>
>--
>Gerry

Groetjes Albert
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