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A277497 Number of cryptarithms of the form x + y = z in base n for which no summand contains any letter more than once and which have at least one solution. 2
3, 49, 1020, 28666, 1099824, 57520786, 3882860433, 331811494082 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

Two cryptarithms are the same if one may be obtained from the other by a process of replacing letters and swapping the summands. For instance, the problem AB + BCD = DDD is the same as ABC + DA = CCC.

Solutions must assign a different digit to each letter, and numbers may not begin with 0.

LINKS

Table of n, a(n) for n=2..9.

Cryptarithms.com, Cryptarithms - Number Puzzles

Math StackExchange, How many strong simple addition mathagrams of degree one are there in a given base?

Eric M. Schmidt, C++ code to compute this sequence

Eric M. Schmidt, List of solvable problems in base 3

EXAMPLE

In base 10, the classic SEND + MORE = MONEY has an assignment of digits to the letters that makes the equation true, and is counted because neither SEND nor MORE contains a given letter more than once.

In base 3, CBA + AB = CAA is solvable, and is counted. There are exactly two solutions: (A = 1, B = 0, C = 2) and (A = 2, B = 0, C = 1).

CROSSREFS

Cf. A277496.

Sequence in context: A203760 A208935 A202534 * A173174 A302466 A303248

Adjacent sequences:  A277494 A277495 A277496 * A277498 A277499 A277500

KEYWORD

nonn,base,hard,more

AUTHOR

Eric M. Schmidt, Oct 18 2016

STATUS

approved

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Last modified January 22 15:13 EST 2022. Contains 350481 sequences. (Running on oeis4.)