Teaser 3315: Primal scream
From The Sunday Times, 5th April 2026 [link] [link]
A fox’s scream woke me in the night. I noted the time on my alarm clock display (hours and minutes) and realised that this number was the product of two prime numbers. (For example, at 01:43, the number 143 is 11×13).
One minute later the numerical time was also the product of two prime numbers. Interestingly, one of the prime numbers at the later time was less than one of the numbers at the earlier time, but these two numbers had the same final two digits in the same order.
At what time did the fox wake me?
[teaser3315]
Frits, 
Ruud, and 
GeoffR and 
John Crabtree and 
Ellen Napier, and 
S2T2 
Jim Randell 6:38 am on 5 April 2026 Permalink |
It is not possible for the times involved to be during the switch to/from daylight savings time, as both 100 and 200 have more than 2 factors.
From the format given in the example (01:43) I am assuming the display is a 24-hour clock.
The following Python program considers displays on a 24-hour clock between 21:00 and 05:59 the following morning.
It runs in 72ms. (Internal runtime is 961µs).
from enigma import (irange, prime_factors, tuples, cproduct, printf) # generate times that are products of <k> primes (21:00 - 05:59) def generate(k): for h in irange(21, 24 + 5): for m in irange(0, 59): # 24 hour clock n = 100*(h % 24) + m fs = list(prime_factors(n)) if len(fs) == k: # return (<minute-count>, <number>, <prime-factors>) yield (60*h + m, n, fs) # consider pairs of times ... for ((t1, n1, fs1), (t2, n2, fs2)) in tuples(generate(2), 2): # separated by 1 minute if not (t2 == t1 + 1): continue # and check the factors for (f1, f2) in cproduct([fs1, fs2]): if not (f1 > f2 > 9 and f1 % 100 == f2 % 100): continue # output solution printf("{n1} {fs1} -> {n2} {fs2}")Solution: [To Be Revealed]
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Ruud 9:36 am on 5 April 2026 Permalink |
import istr from collections import namedtuple istr.int_format("04") candidates = {} for p0, p1 in istr.product(istr.primes(1, 1000), repeat=2): if (hour := (product := (p0 * p1))[:2]) <= 23 and (minute := product[2:]) <= 59 and p0 <= p1 and (hour < 8 or hour > 18): t = hour * 60 + minute candidates[t] = namedtuple("x", "primes time")((p0, p1), hour | ":" | minute) t0 = None for t1 in sorted(candidates): if t0 == t1 - 1 and any(p0x > p1x and p0x[-2:] == p1x[-2:] for p0x in candidates[t0].primes for p1x in candidates[t1].primes): print(candidates[t0].time, *map(int, candidates[t0].primes), candidates[t0].time, *map(int, candidates[t1].primes)) t0 = t1LikeLike
Frits 2:40 pm on 5 April 2026 Permalink |
@Ruud,
“primes(1, 1000)” seems to be too restrictive (eg ignoring time 23:06)
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