A277496 Number of cryptarithms of the form x + y = z in base n for which no summand contains any letter more than once and for which the solution is unique.

3, 43, 909, 25264, 946088, 49916876, 3402999604, 295506405205

Offset

2,1

Comments

Two cryptarithms are the same if one may be obtained from the other by a process of replacing letters and/or 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 uniquely solvable problems in base 3

Example

In base 10, the classic SEND + MORE = MONEY has a unique 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 + CAB = AAA has a unique solution (A = 2, B = 0, C = 1), and so is counted.

Crossrefs

Cf. A277497.

Sequence in context: A350924 A141060 A361878 * A302218 A302664 A201784

Adjacent sequences: A277493 A277494 A277495 * A277497 A277498 A277499

Keyword

nonn,base,hard,more

Author

Eric M. Schmidt, Oct 18 2016

Status

approved