## Teaser 2986: The Prhymes’ Numbers

**From The Sunday Times, 15th December 2019** [link]

The Prhymes’ triple live album “Deified” has hidden numerical “tricks” in the cover notes. Track 1, with the shortest duration, is a one-and-a-half minute introduction of the band, shown as “1. Zak, Bob, Kaz 1:30” in the cover notes. The other nineteen tracks each have different durations under ten minutes and are listed similarly with durations in “m:ss” format.

For each of tracks 2 to 20, thinking of its “m:ss” duration as a three-figure whole number (ignoring the colon), the track number and duration value each have the same number of factors. Curiously, the most possible are palindromic; and the most possible are even.

What is the total album duration (given as m:ss)?

[teaser2986]

## Jim Randell 9:37 pm

on13 December 2019 Permalink |This Python program collect possible numbers corresponding to track times by the number of divisors, and then the required track numbers, also by the number of divisors. It then correlates the lists, maximising the number of palindromes and even numbers. It runs in 78ms.

Run:[ @repl.it ]Solution:The total album duration is 106:01 (i.e. 1 hour, 46 minutes, 1 second).LikeLike