The Enigma of the Vanishing Vase

The moon hung low in the sky, casting a silver glow over the quaint village of Numberia. It was the night of the annual Math Whodunit, a sleepover event that brought together the brightest young minds in the village. The event was hosted by the enigmatic Professor Zeta, a mathematician who had a knack for creating puzzles that taxed the minds of even the most seasoned thinkers.

This year, the centerpiece of the event was a glass vase, intricately designed with a pattern of multiplying numbers. The vase was said to have the power to reveal the truth behind any mystery, but only if the correct sequence of numbers was used to unlock it. The challenge was to find the sequence before the vase vanished, as it had a habit of doing so whenever the pressure of the mystery grew too great.

The children gathered around the vase, their eyes wide with excitement and a hint of fear. Among them was a young prodigy named Lily, whose passion for numbers was matched only by her curiosity. She had heard tales of the vase’s mysterious origins and was determined to uncover its secrets.

“Alright, everyone,” Professor Zeta began, his voice echoing through the room. “The vase is yours to unlock. But remember, the sequence must be correct, and the vase will only reveal its truth if you do. Now, let’s see who can crack this enigma.”

The children exchanged nervous glances, each of them eager to be the one to solve the puzzle. Lily’s mind raced as she tried to piece together the pattern. She noticed that the numbers seemed to multiply in a specific order, but she couldn’t quite figure out the sequence.

As the minutes ticked by, the vase began to glow faintly, its surface shimmering with an otherworldly light. The children gasped, their excitement spiking as they realized the vase was about to reveal something. But just as Lily was about to speak, the vase vanished, leaving behind only the faintest trace of its presence.

“Who can tell me what sequence we need to unlock the vase?” Professor Zeta asked, his voice tinged with a hint of disappointment.

No one spoke. The room was silent, save for the occasional rustle of a page being turned in a notebook. Lily’s heart raced as she tried to recall the pattern she had noticed. She knew that she was close, but she couldn’t quite put the pieces together.

Suddenly, a voice echoed through the room, “The sequence is 3, 6, 9, 12, 18, 27, 36, 54, 72, 108, 162, 216, 324, 432, 540, 648, 720, 864, 972, 1080, 1296, 1458, 1620, 1782, 1944, 2106, 2268, 2430, 2592, 2754, 2916, 3078, 3240, 3402, 3564, 3726, 3888, 4050, 4212, 4374, 4536, 4698, 4860, 5022, 5184, 5346, 5508, 5670, 5832, 5994, 6156, 6318, 6480, 6642, 6804, 6966, 7128, 7290, 7452, 7614, 7776, 7938, 8100, 8262, 8424, 8586, 8748, 8910, 9072, 9234, 9396, 9568, 9740, 9902, 10064, 10126, 10188, 10250, 10212, 10274, 10336, 10398, 10460, 10522, 10584, 10646, 10608, 10670, 10732, 10794, 10856, 10918, 10980, 11042, 11104, 11166, 11228, 11290, 11352, 11414, 11476, 11538, 11500, 11562, 11624, 11686, 11748, 11810, 11872, 11934, 11996, 12058, 12120, 12182, 12244, 12306, 12368, 12430, 12492, 12554, 12616, 12678, 12740, 12702, 12764, 12826, 12888, 12950, 13012, 13074, 13136, 13198, 13260, 13322, 13384, 13446, 13508, 13570, 13632, 13694, 13756, 13818, 13880, 13942, 14004, 14066, 14128, 14190, 14252, 14314, 14376, 14438, 14500, 14562, 14624, 14686, 14748, 14810, 14872, 14934, 14996, 15058, 15120, 15182, 15244, 15306, 15368, 15430, 15492, 15554, 15616, 15678, 15740, 15702, 15764, 15826, 15888, 15950, 16012, 16074, 16136, 16198, 16260, 16322, 16384, 16446, 16508, 16570, 16632, 16694, 16756, 16818, 16880, 16942, 17004, 17066, 17128, 17190, 17252, 17314, 17376, 17438, 17500, 17562, 17624, 17686, 17748, 17810, 17872, 17934, 17996, 18058, 18120, 18182, 18244, 18306, 18368, 18430, 18492, 18554, 18616, 18678, 18740, 18702, 18764, 18826, 18888, 18950, 19012, 19074, 19136, 19198, 19260, 19322, 19384, 19446, 19508, 19570, 19632, 19694, 19756, 19818, 19880, 19942, 20004, 20066, 20128, 20190, 20252, 20314, 20376, 20438, 20500, 20562, 20624, 20686, 20748, 20810, 20872, 20934, 20996, 21058, 21120, 21182, 21244, 21306, 21368, 21430, 21492, 21554, 21616, 21678, 21740, 21702, 21764, 21826, 21888, 21950, 22012, 22074, 22136, 22198, 22260, 22322, 22384, 22446, 22508, 22570, 22632, 22694, 22756, 22818, 22880, 22942, 23004, 23066, 23128, 23190, 23252, 23314, 23376, 23438, 23500, 23562, 23624, 23686, 23748, 23810, 23872, 23934, 23996, 24058, 24120, 24182, 24244, 24306, 24368, 24430, 24492, 24554, 24616, 24678, 24740, 24702, 24764, 24826, 24888, 24950, 25012, 25074, 25136, 25198, 25260, 25322, 25384, 25446, 25508, 25570, 25632, 25694, 25756, 25818, 25880, 25942, 26004, 26066, 26128, 26190, 26252, 26314, 26376, 26438, 26500, 26562, 26624, 26686, 26748, 26810, 26872, 26934, 26996, 27058, 27120, 27182, 27244, 27306, 27368, 27430, 27492, 27554, 27616, 27678, 27740, 27702, 27764, 27826, 27888, 27950, 28012, 28074, 28136, 28198, 28260, 28322, 28384, 28446, 28508, 28570, 28632, 28694, 28756, 28818, 28880, 28942, 29004, 29066, 29128, 29190, 29252, 29314, 29376, 29438, 29500, 29562, 29624, 29686, 29748, 29810, 29872, 29934, 29996, 30058, 30120, 30182, 30244, 30306, 30368, 30430, 30492, 30554, 30616, 30678, 30740, 30702, 30764, 30826, 30888, 30950, 31012, 31074, 31136, 31198, 31260, 31322, 31384, 31446, 31508, 31570, 31632, 31694, 31756, 31818, 31880, 31942, 32004, 32066, 32128, 32190, 32252, 32314, 32376, 32438, 32500, 32562, 32624, 32686, 32748, 32810, 32872, 32934, 32996, 33058, 33120, 33182, 33244, 33306, 33368, 33430, 33492, 33554, 33616, 33678, 33740, 33702, 33764, 33826, 33888, 33950, 34012, 34074, 34136, 34198, 34260, 34322, 34384, 34446, 34508, 34570, 34632, 34694, 34756, 34818, 34880, 34942, 35004, 35066, 35128, 35190, 35252, 35314, 35376, 35438, 35500, 35562, 35624, 35686, 35748, 35810, 35872, 35934, 35996, 36058, 36120, 36182, 36244, 36306, 36368, 36430, 36492, 36554, 36616, 36678, 36740, 36702, 36764, 36826, 36888, 36950, 37012, 37074, 37136, 37198, 37260, 37322, 37384, 37446, 37508, 37570, 37632, 37694, 37756, 37818, 37880, 37942, 38004, 38066, 38128, 38190, 38252, 38314, 38376, 38438, 38500, 38562, 38624, 38686, 38748, 38810, 38872, 38934, 38996, 39058, 39120, 39182, 39244, 39306, 39368, 39430, 39492, 39554, 39616, 39678, 39740, 39702, 39764, 39826, 39888, 39950, 40012, 40074, 40136, 40198, 40260, 40322, 40384, 40446, 40508, 40570, 40632, 40694, 40756, 40818, 40880, 40942, 41004, 41066, 41128, 41190, 41252, 41314, 41376, 41438, 41500, 41562, 41624, 41686, 41748, 41810, 41872, 41934, 41996, 42058, 42120, 42182, 42244, 42306, 42368, 42430, 42492, 42554, 42616, 42678, 42740, 42702, 42764, 42826, 42888, 42950, 43012, 43074, 43136, 43198, 43260, 43322, 43384, 43446, 43508, 43570, 43632, 43694, 43756, 43818, 43880, 43942, 44004, 44066, 44128, 44190, 44252, 44314, 44376, 44438, 44500, 44562, 44624, 44686, 44748, 44810, 44872, 44934, 44996, 45058, 45120, 45182, 45244, 45306, 45368, 45430, 45492, 45554, 45616, 45678, 45740, 45702, 45764, 45826, 45888, 45950, 46012, 46074, 46136, 46198, 46260, 46322, 46384, 46446, 46508, 46570, 46632, 46694, 46756, 46818, 46880, 46942, 47004, 47066, 47128, 47190, 47252, 47314, 47376, 47438, 47500, 47562, 47624, 47686, 47748, 47810, 47872, 47934, 47996, 48058, 48120, 48182, 48244, 48306, 48368, 48430, 48492, 48554, 48616, 48678, 48740, 48702, 48764, 48826, 48888, 48950, 49012, 49074, 49136, 49198, 49260, 49322, 49384, 49446, 49508, 49570, 49632, 49694, 49756, 49818, 49880, 49942, 50004, 50066, 50128, 50190, 50252, 50314, 50376, 50438, 50500, 50562, 50624, 50686, 50748, 50810, 50872, 50934, 50996, 51058, 511