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Best and worst Rarebit numbers

All 1,000,000 numbers are scored with the same rules. Lists are ordered by score, then by number.

Why the best numbers score so high

The top three are 999,999 (587), 2,048 (560), 2,223 (505). A score adds the best badge from each of six families, so the leaders are unusual in four or five ways at once: a culture badge worth 199 points, a rare shape such as a power of two or a Kaprekar number, a string found in π, e or φ, and a calendar badge. Repeated patterns in the same family do not stack.

At the bottom, 179,035 numbers earn no badge and score 0, all sharing rank 820,966. The smallest of them is 1,281; every number below it earns at least one badge.

Top 100

The 100 highest-scoring Rarebit numbers
RankNumberScoreTiesCounting badges (points)
1999,999587—Solid Block 144, Kaprekar's Trick 143, Pi Wedge 101, Top Shelf 199
22,048560—Even Keel 60, Square Pair 22, Doubling Up 156, Year Marker 123, Tile Merger 199
32,223505—Nine Sum 90, Prime Parts 75, Kaprekar's Trick 143, Golden Crumb 102, Clock Face 95
413466—Odd Squad 57, Twin Star 59, Golden Spiral 151, Baker's Dozen 199
5777452—Solid Block 144, Prime Parts 75, Digit Divider 34, Sevens Row 199
6100429—Double Take 13, Square Pair 22, Square Deal 100, Clock Face 95, Hundred Club 199
71,331420—Mirror Image 90, Cubed 133, Euler Crumb 102, Clock Face 95
82,304409—Nine Sum 90, Square Pair 22, Square Deal 100, Golden Crumb 102, Clock Face 95
91,000400—Triple Stack 48, Square Pair 22, Cubed 133, Pi Crumb 102, Clock Face 95
109,999389—Solid Block 144, Kaprekar's Trick 143, Pi Crumb 102
1199,999388—Solid Block 144, Kaprekar's Trick 143, Pi Bite 101
121,001384—Mirror Image 90, Clock Face 95, Thousand Nights 199
131,953377—Odd Squad 57, Triangle Stack 95, Pi Crumb 102, Year Marker 123
14720375—Nine Sum 90, Square Pair 22, Factorial Flash 168, Clock Face 95
151,337374—Odd Squad 57, Two Factors 23, Clock Face 95, Elite Code 199
161,936373—No Repeats 26, Square Pair 22, Square Deal 100, Euler Crumb 102, Year Marker 123
171,711372—Odd Squad 57, Two Factors 23, Triangle Stack 95, Golden Crumb 102, Clock Face 95
182,034371Tied with 1Nine Sum 90, Square Pair 22, Digit Divider 34, Golden Crumb 102, Year Marker 123
182,061371Tied with 1Nine Sum 90, Square Pair 22, Digit Divider 34, Pi Crumb 102, Year Marker 123
2055370—Solid Block 144, Prime Parts 75, Golden Spiral 151
217365—Odd Squad 57, Prime Parts 75, Digit Divider 34, Seventh Heaven 199
227,777362Tied with 1Solid Block 144, Prime Parts 75, Kaprekar's Trick 143
2222,222362Tied with 1Solid Block 144, Prime Parts 75, Kaprekar's Trick 143
24225360—Nine Sum 90, Prime Parts 75, Square Deal 100, Clock Face 95
25314,159359—Twin Star 59, Pi Wedge 101, Pi Opening 199
26144358—Nine Sum 90, Square Pair 22, Golden Spiral 151, Clock Face 95
272,007349Tied with 1Nine Sum 90, Digit Divider 34, Euler Crumb 102, Year Marker 123
272,070349Tied with 1Nine Sum 90, Digit Divider 34, Golden Crumb 102, Year Marker 123
29222348Tied with 2Solid Block 144, Prime Parts 75, Digit Divider 34, Clock Face 95
29333348Tied with 2Solid Block 144, Prime Parts 75, Digit Divider 34, Clock Face 95
29555348Tied with 2Solid Block 144, Prime Parts 75, Digit Divider 34, Clock Face 95
321,849346—No Repeats 26, Two Factors 23, Square Deal 100, Euler Crumb 102, Clock Face 95
3390,000345Tied with 2Nine Sum 90, Square Pair 22, Square Deal 100, Round Ten Thousand 133
33360,000345Tied with 2Nine Sum 90, Square Pair 22, Square Deal 100, Round Ten Thousand 133
33810,000345Tied with 2Nine Sum 90, Square Pair 22, Square Deal 100, Round Ten Thousand 133
361,017343Tied with 7Nine Sum 90, Square Pair 22, Digit Divider 34, Golden Crumb 102, Clock Face 95
361,044343Tied with 7Nine Sum 90, Square Pair 22, Digit Divider 34, Golden Crumb 102, Clock Face 95
361,125343Tied with 7Nine Sum 90, Square Pair 22, Digit Divider 34, Euler Crumb 102, Clock Face 95
361,224343Tied with 7Nine Sum 90, Square Pair 22, Digit Divider 34, Pi Crumb 102, Clock Face 95
361,332343Tied with 7Nine Sum 90, Square Pair 22, Digit Divider 34, Euler Crumb 102, Clock Face 95
361,530343Tied with 7Nine Sum 90, Square Pair 22, Digit Divider 34, Euler Crumb 102, Clock Face 95
361,620343Tied with 7Nine Sum 90, Square Pair 22, Digit Divider 34, Golden Crumb 102, Clock Face 95
361,800343Tied with 7Nine Sum 90, Square Pair 22, Digit Divider 34, Golden Crumb 102, Clock Face 95
441,931341Tied with 1Odd Squad 57, Twin Star 59, Pi Crumb 102, Year Marker 123
442,000341Tied with 1Even Keel 60, Square Pair 22, Digit Divider 34, Pi Crumb 102, Year Marker 123
4610,000340Tied with 5Tower of Four 85, Square Pair 22, Square Deal 100, Round Ten Thousand 133
4640,000340Tied with 5Tower of Four 85, Square Pair 22, Square Deal 100, Round Ten Thousand 133
46160,000340Tied with 5Tower of Four 85, Square Pair 22, Square Deal 100, Round Ten Thousand 133
46250,000340Tied with 5Tower of Four 85, Square Pair 22, Square Deal 100, Round Ten Thousand 133
46490,000340Tied with 5Tower of Four 85, Square Pair 22, Square Deal 100, Round Ten Thousand 133
46640,000340Tied with 5Tower of Four 85, Square Pair 22, Square Deal 100, Round Ten Thousand 133
522,025335Tied with 1Nine Sum 90, Square Pair 22, Square Deal 100, Year Marker 123
522,346335Tied with 1Uphill Climb 43, Triangle Stack 95, Pi Crumb 102, Clock Face 95
54233334—Double Take 13, Prime Parts 75, Golden Spiral 151, Clock Face 95
551,600332Tied with 1Double Take 13, Square Pair 22, Square Deal 100, Golden Crumb 102, Clock Face 95
5517,711332Tied with 1Odd Squad 57, Two Factors 23, Golden Spiral 151, Golden Bite 101
5727,000323Tied with 1Nine Sum 90, Cubed 133, Round Thousand 100
57216,000323Tied with 1Nine Sum 90, Cubed 133, Round Thousand 100
591,134321Tied with 4Nine Sum 90, Digit Divider 34, Pi Crumb 102, Clock Face 95
591,323321Tied with 4Nine Sum 90, Digit Divider 34, Euler Crumb 102, Clock Face 95
591,710321Tied with 4Nine Sum 90, Digit Divider 34, Pi Crumb 102, Clock Face 95
592,115321Tied with 4Nine Sum 90, Digit Divider 34, Golden Crumb 102, Clock Face 95
592,133321Tied with 4Nine Sum 90, Digit Divider 34, Pi Crumb 102, Clock Face 95
64216318Tied with 4Nine Sum 90, Cubed 133, Clock Face 95
64343318Tied with 4Mirror Image 90, Cubed 133, Clock Face 95
641,540318Tied with 4No Repeats 26, Triangle Stack 95, Euler Crumb 102, Clock Face 95
641,653318Tied with 4No Repeats 26, Triangle Stack 95, Golden Crumb 102, Clock Face 95
641,830318Tied with 4No Repeats 26, Triangle Stack 95, Pi Crumb 102, Clock Face 95
698,000315Tied with 1Even Keel 60, Square Pair 22, Cubed 133, Round Thousand 100
6964,000315Tied with 1Even Keel 60, Square Pair 22, Cubed 133, Round Thousand 100
712,222314Tied with 1Solid Block 144, Prime Parts 75, Clock Face 95
713,600314Tied with 1Nine Sum 90, Square Pair 22, Square Deal 100, Pi Crumb 102
731,319313Tied with 6Odd Squad 57, Twin Star 59, Golden Crumb 102, Clock Face 95
73100,000313Tied with 6Tower of Five 124, Square Pair 22, Digit Divider 34, Round Ten Thousand 133
73200,000313Tied with 6Tower of Five 124, Square Pair 22, Digit Divider 34, Round Ten Thousand 133
73400,000313Tied with 6Tower of Five 124, Square Pair 22, Digit Divider 34, Round Ten Thousand 133
73500,000313Tied with 6Tower of Five 124, Square Pair 22, Digit Divider 34, Round Ten Thousand 133
73800,000313Tied with 6Tower of Five 124, Square Pair 22, Digit Divider 34, Round Ten Thousand 133
73900,000313Tied with 6Tower of Five 124, Square Pair 22, Digit Divider 34, Round Ten Thousand 133
802,083310Tied with 2No Repeats 26, Twin Star 59, Pi Crumb 102, Year Marker 123
802,087310Tied with 2No Repeats 26, Twin Star 59, Golden Crumb 102, Year Marker 123
802,089310Tied with 2No Repeats 26, Twin Star 59, Pi Crumb 102, Year Marker 123
834,005309—Nine Sum 90, Square Pair 22, Triangle Stack 95, Golden Crumb 102
84121308Tied with 1Mirror Image 90, Two Factors 23, Square Deal 100, Clock Face 95
842,016308Tied with 1Nine Sum 90, Triangle Stack 95, Year Marker 123
86324307Tied with 3Nine Sum 90, Square Pair 22, Square Deal 100, Clock Face 95
86441307Tied with 3Nine Sum 90, Square Pair 22, Square Deal 100, Clock Face 95
86900307Tied with 3Nine Sum 90, Square Pair 22, Square Deal 100, Clock Face 95
861,521307Tied with 3Nine Sum 90, Square Pair 22, Square Deal 100, Clock Face 95
902,353306—Prime Parts 75, Digit Divider 34, Pi Crumb 102, Clock Face 95
911,957305Tied with 1Odd Squad 57, Two Factors 23, Pi Crumb 102, Year Marker 123
911,959305Tied with 1Odd Squad 57, Two Factors 23, Pi Crumb 102, Year Marker 123
932,111304—Triple Stack 48, Twin Star 59, Euler Crumb 102, Clock Face 95
942303Tied with 3Even Keel 60, Prime Parts 75, Factorial Flash 168
94125,000303Tied with 3Triple Stack 48, Square Pair 22, Cubed 133, Round Thousand 100
94512,000303Tied with 3Triple Stack 48, Square Pair 22, Cubed 133, Round Thousand 100
94729,000303Tied with 3Triple Stack 48, Square Pair 22, Cubed 133, Round Thousand 100
98153302—Nine Sum 90, Square Pair 22, Triangle Stack 95, Clock Face 95
992,772301Tied with 1Mirror Image 90, Prime Parts 75, Digit Divider 34, Euler Crumb 102
993,222301Tied with 1Nine Sum 90, Prime Parts 75, Digit Divider 34, Golden Crumb 102

Bottom 100

All of these score 0. With 179,035 numbers tied at the bottom (Bottom 17.91%), this list shows the 100 smallest.

The 100 smallest numbers with the lowest Rarebit score
RankNumberScoreTiesCounting badges (points)
820,9661,2810Tied with 179,034None
820,9661,2920Tied with 179,034None
820,9661,4640Tied with 179,034None
820,9661,4740Tied with 179,034None
820,9661,4840Tied with 179,034None
820,9661,4910Tied with 179,034None
820,9661,5810Tied with 179,034None
820,9661,6860Tied with 179,034None
820,9661,8680Tied with 179,034None
820,9661,8780Tied with 179,034None
820,9662,3820Tied with 179,034None
820,9662,3920Tied with 179,034None
820,9662,4140Tied with 179,034None
820,9662,4320Tied with 179,034None
820,9662,4540Tied with 179,034None
820,9662,4720Tied with 179,034None
820,9662,4920Tied with 179,034None
820,9662,5240Tied with 179,034None
820,9662,5260Tied with 179,034None
820,9662,5420Tied with 179,034None
820,9662,5650Tied with 179,034None
820,9662,5850Tied with 179,034None
820,9662,5950Tied with 179,034None
820,9662,6160Tied with 179,034None
820,9662,6320Tied with 179,034None
820,9662,6360Tied with 179,034None
820,9662,6520Tied with 179,034None
820,9662,6720Tied with 179,034None
820,9662,6760Tied with 179,034None
820,9662,7020Tied with 179,034None
820,9662,7170Tied with 179,034None
820,9662,7260Tied with 179,034None
820,9662,7820Tied with 179,034None
820,9662,8320Tied with 179,034None
820,9662,8520Tied with 179,034None
820,9662,8720Tied with 179,034None
820,9662,8920Tied with 179,034None
820,9662,8980Tied with 179,034None
820,9662,9280Tied with 179,034None
820,9662,9720Tied with 179,034None
820,9662,9790Tied with 179,034None
820,9663,0100Tied with 179,034None
820,9663,0400Tied with 179,034None
820,9663,0900Tied with 179,034None
820,9663,2120Tied with 179,034None
820,9663,2300Tied with 179,034None
820,9663,2340Tied with 179,034None
820,9663,2430Tied with 179,034None
820,9663,2620Tied with 179,034None
820,9663,2830Tied with 179,034None
820,9663,2920Tied with 179,034None
820,9663,4040Tied with 179,034None
820,9663,4230Tied with 179,034None
820,9663,4240Tied with 179,034None
820,9663,4830Tied with 179,034None
820,9663,4840Tied with 179,034None
820,9663,5340Tied with 179,034None
820,9663,5650Tied with 179,034None
820,9663,5850Tied with 179,034None
820,9663,6060Tied with 179,034None
820,9663,6300Tied with 179,034None
820,9663,6320Tied with 179,034None
820,9663,6380Tied with 179,034None
820,9663,6760Tied with 179,034None
820,9663,6860Tied with 179,034None
820,9663,7030Tied with 179,034None
820,9663,7360Tied with 179,034None
820,9663,8080Tied with 179,034None
820,9663,8300Tied with 179,034None
820,9663,8350Tied with 179,034None
820,9663,8360Tied with 179,034None
820,9663,8380Tied with 179,034None
820,9663,8430Tied with 179,034None
820,9663,8780Tied with 179,034None
820,9663,9320Tied with 179,034None
820,9663,9340Tied with 179,034None
820,9663,9380Tied with 179,034None
820,9664,0300Tied with 179,034None
820,9664,0470Tied with 179,034None
820,9664,0740Tied with 179,034None
820,9664,1240Tied with 179,034None
820,9664,1340Tied with 179,034None
820,9664,1420Tied with 179,034None
820,9664,1470Tied with 179,034None
820,9664,1540Tied with 179,034None
820,9664,1640Tied with 179,034None
820,9664,1910Tied with 179,034None
820,9664,2140Tied with 179,034None
820,9664,2540Tied with 179,034None
820,9664,2720Tied with 179,034None
820,9664,3140Tied with 179,034None
820,9664,3240Tied with 179,034None
820,9664,3400Tied with 179,034None
820,9664,3450Tied with 179,034None
820,9664,3470Tied with 179,034None
820,9664,3480Tied with 179,034None
820,9664,3540Tied with 179,034None
820,9664,3830Tied with 179,034None
820,9664,5040Tied with 179,034None
820,9664,5240Tied with 179,034None

Score histogram

287 different scores occur. Most numbers score under 50; very few pass 300.

How many of the 1,000,000 numbers fall in each score range
ScoreNumbersShareBar
0179,03517.9%
1–49612,32961.23%
50–99176,64117.66%
100–14925,9732.6%
150–1994,8120.48%
200–2498560.09%
250–2992530.03%
300–349750.01%
350–399170%
400–44940%
450–49920%
500–54910%
550–59920%