#math trivia for #September3: #246 has an “even-digit-count” of 3. What even-digit-count occurs most often among day-numbers (1-365)?

— Burt Kaliski Jr. (@modulomathy) September 4, 2013

Intuitively, I’d guess that the most frequent even-digit-count is probably 1, because that’s what it would be for two-digit numbers, as well as numbers in the 100-199 and 300-365 ranges. Only numbers in the 200-299 range would be more likely to have an even-digit-count of 2. (Numbers in the smaller 1-9 range would be more likely to have an even-digit-count of 0.)

Let’s see if this works:

Range | Even-digit-count = 0 | = 1 | = 2 | = 3 |

1-9 | 5 | 4 | 0 | 0 |

10-99 | 25 | 45 | 20 | 0 |

100-199 | 25 | 50 | 25 | 0 |

200-299 | 0 | 25 | 50 | 25 |

300-365 | 15 | 33 | 18 | 0 |

Total | 70 | 157 | 113 | 25 |

The intuition is correct: an even-digit-count of 1 is the most likely.