Sunday Times Teaser 3323 – Planet 9 from outer space
by Stephen Hogg
Published Sunday May 31 2026 (link)
T’zer was the ninth planet of the Sol-Vit system. Over time, astronomers on T’zer observed each of the eight innermost planets when the lines from the sun to the planet and the planet to T’zer were perpendicular. Radar showed the eight T’zer-to-planet distances at these positions were different whole numbers of light-chrons. Simultaneously, measuring the angle between the sun’s centre and the planet, they then calculated each planet’s distance from the sun (they were all whole numbers of light-chrons). T’zer’s calculated distance from the sun was always the same whole number of light-chrons due to its circular orbit.
Astrologers grumbled about this latter distance being under the 80 light-chrons used, historically, when producing horoscopes.
What is T’zer’s distance from its sun (in light-chrons)?
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BRG permalink12345678910111213141516# consider the radius for T'zerfor r in range(1, 80):r2s = dict()# construct right angled triangles on T'zer's# radius and collect side valuesfor x in range(1, r):y2 = (r * r - x * x)if (y := round((y2 ** 0.5))) ** 2 == y2:r2s[r] = r2s.get(r, set()) | {x, y}# find a radius that gives eight different sidesfor r, ss in r2s.items():if len(ss) == 8:print(f"T'zers radius = {r} ({ss}.")
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Frits permalink1234567891011121314151617181920from math import isqrtdef is_sq(x):return isqrt(x) ** 2 == x# T'zer's distance from its sunfor t in range(9, 80):# calculate each planet's distance from the sunds = set()for x in range(1, int(((t2 := t * t) / 2)**.5) + 1):if is_sq(t2 - x * x):y = int((t2 - x * x)**.5)ds.add((x, y))ds.add((y, x))# can we identify at least eight innermost planets?if len(ds) > 7:print(f"answer: {t} light-chrons")
