Mike: Perhaps this is already known, but what about long division puzzles which have unique solutions *for each radix*, but can be (uniquely) solved for multiple radices (radishes?) ? BTW, one of the early claims for the Prolog programming language was its ability to "trivially" solve digit arithmetic puzzles; Prolog automatically performed "hypothesize & test" for you, with builtin backtracking when an hypothesis failed. At 10:41 AM 1/18/2019, Mike Beeler wrote:
One last twist on the Foxtrot long division alphametric puzzle. The original has 16 digit positions. I think it can be reduced to 14, and still have a non-trivial puzzle that illustrates the operations in long division. I suggest this "mini-Foxtrot" puzzle: (fixed width font needed)
C D 2 4 ---------- ---------- A B ) B A C 1 3 ) 3 1 2 C E 2 6 ---- ---- F C 5 2 F C 5 2 ---- ---- Z 0
In looking for puzzles with few digit positions, a lot of simple cases arise, such as "121 / 11 = 11", "144 / 12 = 12", etc. That made me wonder what might be the *hardest* puzzles. I suspect those that use all ten digits are hardest. Below are the 4 of original Foxtrot structure, and the 2 of mini-Foxtrot. Each has a unique solution.
C D ---------- A B ) E F G H I ---- A A G A A G ------- Z
C D ---------- A B ) E Z F G H ---- A I F A I F ------- Z
C D ---------- A B ) E F C G H ---- F I C F I C ------- Z
C D ---------- A B ) B A E F G ---- H I E H I E ------- Z
C D ---------- A B ) E F G E H ---- I G I G ---- Z
C D ---------- A B ) D E F G H ---- I F I F ---- Z
SPOILER ALERT 592 / 16 = 37 702 / 18 = 39 912 / 38 = 24 936 / 39 = 24 598 / 13 = 46 456 / 19 = 24
-- Mike
On Jan 13, 2019, at 5:39 PM, rcs@xmission.com wrote:
There's a cute puzzle at
https://www.foxtrot.com/2019/01/13/cell-division/
I get a unique answer. Perhaps the smallest such puzzle?
Rich