As hinted by the title, flavortext, and repeated uses of Number as a proper noun, the clues describe Yu-Gi-Oh! Xyz monsters of the "Number" archetype. This puzzle uses the base versions of every number from Numbers 5 through 107 (no Numeron Gates, no "Number C", "Number S", or "Number F" monsters, no other versions of "Number 39: Utopia", and no "Number XX: Utopic Dark Infinity"). Applying the math operations produces a new Number, and as stated in the flavortext, every Number appears at most once, except one which appears twice. The Numbers obtained from the clues, and the Numbers resulting from performing the arithmetic operations are as follows:
| Number 1 | Number 2 | Result | ||
|---|---|---|---|---|
| Number 61: Volcasaurus | - | Number 56: Gold Rat | = | Number 5: Doom Chimera Dragon |
| Number 66: Master Key Beetle | - | Number 9: Dyson Sphere | = | Number 57: Tri-Head Dust Dragon |
| Number 20: Giga-Brilliant | + | Number 25: Force Focus | = | Number 45: Crumble Logos the Prophet of Demolition |
| Number 31: Embodiment of Punishment | + | Number 33: Chronomaly Machu Mech | = | Number 64: Ronin Raccoon Sandayu |
| Number 74: Master of Blades | + | Number 29: Mannequin Cat | = | Number 103: Ragnazero |
| Number 93: Utopia Kaiser | - | Number 38: Hope Harbinger Dragon Titanic Galaxy | = | Number 55: Gogogo Goliath |
| Number 99: Utopic Dragon | - | Number 47: Nightmare Shark | = | Number 52: Diamond Crab King |
| Number 88: Gimmick Puppet of Leo | - | Number 40: Gimmick Puppet of Strings | = | Number 48: Shadow Lich |
| Number 94: Crystalzero | - | Number 70: Malevolent Sin | = | Number 24: Dragulas the Vampiric Dragon |
| Number 83: Galaxy Queen | - | Number 21: Frozen Lady Justice | = | Number 62: Galaxy-Eyes Prime Photon Dragon |
| Number 12: Crimson Shadow Armor Ninja | x | Number 8: Heraldic King Genom-Heritage | = | Number 96: Dark Mist |
| Number 95: Galaxy-Eyes Dark Matter Dragon | - | Number 72: Shogi Rook | = | Number 23: Lancelot, Dark Knight of the Underworld |
| Number 67: Pair-a-Dice Smasher | - | Number 13: Embodiment of Crime | = | Number 54: Lion Heart |
| Number 71: Rebarian Shark | - | Number 53: Heart-eartH | = | Number 18: Heraldry Patriarch |
| Number 80: Rhapsody in Berserk | - | Number 34: Terror-byte | = | Number 46: Dragluon |
| Number 101: Silent Honor ARK | - | Number 87: Queen of the Night | = | Number 14: Greedy Sarameya |
| Number 65: Djinn Buster | + | Number 11: Big Eye | = | Number 76: Harmonizer Gradielle |
| Number 106: Giant Hand | - | Number 17: Leviathan Dragon | = | Number 89: Diablosis the Mind Hacker |
| Number 43: Manipulator of Souls | - | Number 7: Lucky Straight | = | Number 36: Chronomaly Chateau Huyuk |
| Number 82: Heartlandraco | - | Number 50: Blackship of Corn | = | Number 32: Shark Drake |
| Number 37: Hope Woven Dragon Spider Shark | + | Number 42: Galaxy Tomahawk | = | Number 79: Battlin’ Boxer Nova Kaiser |
| Number 39: Utopia | + | Number 58: Burner Visor | = | Number 97: Draglubion |
| Number 91: Thunder Spark Dragon | - | Number 69: Heraldry Crest | = | Number 22: Zombiestein |
| Number 85: Crazy Box | - | Number 59: Crooked Cook | = | Number 26: Spaceway Octobypass |
| Number 78: Number Archive | - | Number 10: Illumiknight | = | Number 68: Sanaphond the Sky Prison |
| Number 107: Galaxy-Eyes Tachyon Dragon | - | Number 77: The Seven Sins | = | Number 30: Acid Golem of Destruction |
| Number 100: Numeron Dragon | - | Number 84: Pain Gainer | = | Number 16: Shock Master |
| Number 102: Star Seraph Sentry | - | Number 27: Dreadnought Dreadnoid | = | Number 75: Bamboozling Gossip Shadow |
| Number 51: Finisher the Strong Arm | + | Number 35: Ravenous Tarantula | = | Number 86: Heroic Champion - Rhongomyniad |
| Number 73: Abyss Splash | + | Number 19: Freezadon | = | Number 92: Heart-eartH Dragon |
| Number 98: Antitopian | - | Number 41: Bagooska the Terribly Tired Tapir | = | Number 57: Tri-Head Dust Dragon |
| SQUARE_ROOT(Number 49: Fortune Tune | x | Number 81:Superdreadnought Rail Cannon Super Dora) | = | Number 63: Shamoji Soldier |
| Number 104: Masquerade | - | Number 44: Sky Pegasus | = | Number 60: Dugales the Timeless |
| Number 105: Battlin' Boxer Star Cestus | - | Number 15: Gimmick Puppet Giant Grinder | = | Number 90: Galaxy-Eyes Photon Lord |
Each of these monsters, in addition to the number in its name, has another important number: its Rank, which is denoted by the number of stars between its name and card art. These stars match the ones given in the puzzle. (Solvers casually familiar with Yu-Gi-Oh may know this as Level, but Xyz monsters have a Rank instead of a Level. Both "rank" and "level" are mentioned in the flavortext.) The next step is to index into the names of the right-hand side Numbers by their ranks:
| Number Name (after the colon) | Rank | Indexed Letter |
|---|---|---|
| DOOM CHIMERA DRAGON | 5 | C |
| TRI-HEAD DUST DRAGON | 4 | H |
| CRUMBLE LOGOS THE PROPHET OF DEMOLITION | 2 | R |
| RONIN RACCOON SANDAYU | 2 | O |
| RAGNAZERO | 4 | N |
| GOGOGO GOLIATH | 4 | O |
| DIAMOND CRAB KING | 4 | M |
| SHADOW LICH | 3 | A |
| DRAGULAS THE VAMPIRIC DRAGON | 6 | L |
| GALAXY-EYES PRIME PHOTON DRAGON | 8 | Y |
| DARK MIST | 2 | A |
| LANCELOT, DARK KNIGHT OF THE UNDERWORLD | 8 | T |
| LION HEART | 1 | L |
| HERALDRY PATRIARCH | 4 | A |
| DRAGLUON | 8 | N |
| GREEDY SARAMEYA | 5 | D |
| HARMONIZER GRADIELLE | 7 | I |
| DIABLOSIS THE MIND HACKER | 7 | S |
| CHRONOMALY CHATEAU HUYUK | 4 | O |
| SHARK DRAKE | 4 | R |
| BATTLIN’ BOXER NOVA KAISER | 4 | T |
| DRAGLUBION | 8 | I |
| ZOMBIESTEIN | 8 | T |
| SPACEWAY OCTOBYPASS | 3 | A |
| SANAPHOND THE SKY PRISON | 8 | N |
| ACID GOLEM OF DESTRUCTION | 3 | I |
| SHOCK MASTER | 4 | C |
| BAMBOOZLING GOSSIP SHADOW | 3 | M |
| HEROIC CHAMPION - RHONGOMYNIAD | 4 | O |
| HEART-EARTH DRAGON | 9 | T |
| TRI-HEAD DUST DRAGON | 4 | H |
| SHAMOJI SOLDIER | 1 | S |
| DUGALES THE TIMELESS | 4 | A |
| GALAXY-EYES PHOTON LORD | 8 | Y |
The resulting cluephrase is CHRONOMALY ATLANDIS OR TITANIC MOTH, SAY. This refers to Number 6: Chronomaly Atlandis and Number 28: Titanic Moth, which are the only Numbers between 5 and 107 that have not appeared in the equations above. Since 6 and 28 are both examples of perfect numbers, the answer is PERFECT. This is subtly confirmed by having 7 stars at the end of the puzzle, indicating a seven letter answer, which excludes less-specific answers like TRIANGULAR, TRIANGLE, and HEXAGONAL.
As someone who likes both math and Yu-Gi-Oh, I wanted to make a puzzle using the Number cards. I figured that the answer "PERFECT" would be, well, perfect for this puzzle, and it was nice to be able to clue the answer by referring to two of the cards. Initially, I wasn't going to use all the Numbers between 5 and 107, but once I realized I was pretty close to doing so with the long cluephrase, I wanted to try to see if it was possible. It took me a while to get a set of arithmetic equations that worked out and used every Number exactly once, but I was very pleased with the final result. Unfortunately, Number 57: Tri-Head Dust Dragon had to be used twice because it's the only Number whose rank indexes the letter "H", which appears twice in the cluephrase. Numbers 1 through 4 existed in the anime (in fact, there were 2 of each, a real Number and a fake Number), but none of these 8 cards have actually been printed in the TCG. The images in the Yu-Gi-Oh wiki are screenshots of the anime, not real cards, so we only have Numbers 5 to 107.
Cluing the Numbers, most of which have unusual names, with "Something Different"-style clues was pretty fun. I sort of cheated by using the word "dragon" in the clues when it is also in the Number names, but I couldn't think of a good way to avoid this.
A number of solvers (pun intended) got stuck on final extraction, trying to find shared properties of the Number Monsters instead of the numbers 6 and 28. The question asked in the beginning asked about numbers, lowercase, to indicate the final answer was about mathematical numbers, but we could have made this clearer.