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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. 2
3, 43, 909, 25264, 946088, 49916876, 3402999604, 295506405205 (list; graph; refs; listen; history; text; internal format)



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.


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


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.


Cf. A277497.

Sequence in context: A299506 A350924 A141060 * A302218 A302664 A201784

Adjacent sequences: A277493 A277494 A277495 * A277497 A277498 A277499




Eric M. Schmidt, Oct 18 2016



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Last modified December 8 11:05 EST 2022. Contains 358693 sequences. (Running on oeis4.)