##
*Koroluka*
(Awk34)

### Level 4

### Solved 100 out of 366

### Click on any of the problems I have solved below to view the solution:

1
Problem 1"Add all the natural numbers below one thousand that are multiples of 3 or 5." |
2
Problem 2"By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms." |
3
Problem 3"Find the largest prime factor of a composite number." |
4
Problem 4"Find the largest palindrome made from the product of two 3-digit numbers." |
5
Problem 5"What is the smallest number divisible by each of the numbers 1 to 20?" |
6
Problem 6"What is the difference between the sum of the squares and the square of the sums?" |
7
Problem 7"Find the 10001st prime." |
8
Problem 8"Discover the largest product of five consecutive digits in the 1000-digit number." |
9
Problem 9"Find the only Pythagorean triplet, { a, b, c}, for which a + b + c = 1000." |
10
Problem 10"Calculate the sum of all the primes below two million." |
11
Problem 11"What is the greatest product of four adjacent numbers on the same straight line in the 20 by 20 grid?" |
12
Problem 12"What is the value of the first triangle number to have over five hundred divisors?" |
13
Problem 13"Find the first ten digits of the sum of one-hundred 50-digit numbers." |
14
Problem 14"Find the longest sequence using a starting number under one million." |
15
Problem 15"Starting in the top left corner in a 20 by 20 grid, how many routes are there to the bottom right corner?" |
16
Problem 16"What is the sum of the digits of the number 2 ^{1000}?" |
17
Problem 17"How many letters would be needed to write all the numbers in words from 1 to 1000?" |
18
Problem 18"Find the maximum sum travelling from the top of the triangle to the base." |
19
Problem 19"How many Sundays fell on the first of the month during the twentieth century?" |
20
Problem 20"Find the sum of digits in 100!" |
21
Problem 21"Evaluate the sum of all amicable pairs under 10000." |
22
Problem 22"What is the total of all the name scores in the file of first names?" |
23
Problem 23"Find the sum of all the positive integers which cannot be written as the sum of two abundant numbers." |
24
Problem 24"What is the millionth lexicographic permutation of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9?" |
25
Problem 25"What is the first term in the Fibonacci sequence to contain 1000 digits?" |

26
Problem 26"Find the value of d < 1000 for which 1/d contains the longest recurring cycle." |
27
Problem 27"Find a quadratic formula that produces the maximum number of primes for consecutive values of n." |
28
Problem 28"What is the sum of both diagonals in a 1001 by 1001 spiral?" |
29
Problem 29"How many distinct terms are in the sequence generated by a for 2 ≤ ^{b}a ≤ 100 and 2 ≤ b ≤ 100?" |
30
Problem 30"Find the sum of all the numbers that can be written as the sum of fifth powers of their digits." |
31
Problem 31"Investigating combinations of English currency denominations." |
32
Problem 32"Find the sum of all numbers that can be written as pandigital products." |
33
Problem 33"Discover all the fractions with an unorthodox cancelling method." |
34
Problem 34"Find the sum of all numbers which are equal to the sum of the factorial of their digits." |
35
Problem 35"How many circular primes are there below one million?" |
36
Problem 36"Find the sum of all numbers less than one million, which are palindromic in base 10 and base 2." |
37
Problem 37"Find the sum of all eleven primes that are both truncatable from left to right and right to left." |
38
Problem 38"What is the largest 1 to 9 pandigital that can be formed by multiplying a fixed number by 1, 2, 3, ... ?" |
39
Problem 39"If p is the perimeter of a right angle triangle, {a, b, c}, which value, for p ≤ 1000, has the most solutions?" |
40
Problem 40"Finding the n^{th} digit of the fractional part of the irrational number." |
41
Problem 41"What is the largest n-digit pandigital prime that exists?" |
42
Problem 42"How many triangle words does the list of common English words contain?" |
43
Problem 43"Find the sum of all pandigital numbers with an unusual sub-string divisibility property." |
44
Problem 44"Find the smallest pair of pentagonal numbers whose sum and difference is pentagonal." |
45
Problem 45"After 40755, what is the next triangle number that is also pentagonal and hexagonal?" |
46
Problem 46"What is the smallest odd composite that cannot be written as the sum of a prime and twice a square?" |
47
Problem 47"Find the first four consecutive integers to have four distinct primes factors." |
48
Problem 48"Find the last ten digits of 1 ^{1} + 2^{2} + ... + 1000^{1000}." |
49
Problem 49"Find arithmetic sequences, made of prime terms, whose four digits are permutations of each other." |
50
Problem 50"Which prime, below one-million, can be written as the sum of the most consecutive primes?" |

51
Problem 51"Find the smallest prime which, by changing the same part of the number, can form eight different primes." |
52
Problem 52"Find the smallest positive integer, x, such that 2x, 3x, 4x, 5x, and 6x, contain the same digits in some order." |
53
Problem 53"How many values of C( n,r), for 1 ≤ n ≤ 100, exceed one-million?" |
54
Problem 54"How many hands did player one win in the game of poker?" |
55
Problem 55"How many Lychrel numbers are there below ten-thousand?" |
56
Problem 56"Considering natural numbers of the form, a, finding the maximum digital sum."^{b} |
57
Problem 57"Investigate the expansion of the continued fraction for the square root of two." |
58
Problem 58"Investigate the number of primes that lie on the diagonals of the spiral grid." |
59
Problem 59"Using a brute force attack, can you decrypt the cipher using XOR encryption?" |
60
Problem 60"Find a set of five primes for which any two primes concatenate to produce another prime." |
61
Problem 61"Find the sum of the only set of six 4-digit figurate numbers with a cyclic property." |
62
Problem 62"Find the smallest cube for which exactly five permutations of its digits are cube." |
63
Problem 63"How many n-digit positive integers exist which are also an n^{th} power?" |
64
Problem 64"How many continued fractions for N ≤ 10000 have an odd period?" |
65
Problem 65"Find the sum of digits in the numerator of the 100 ^{th} convergent of the continued fraction for e." |
66
Problem 66"Investigate the Diophantine equation x^{2} − Dy^{2} = 1." |
67
Problem 67"Using an efficient algorithm find the maximal sum in the triangle?" |
68
Problem 68"What is the maximum 16-digit string for a "magic" 5-gon ring?" |
69
Problem 69"Find the value of n ≤ 1,000,000 for which n/φ(n) is a maximum." |
70
Problem 70"Investigate values of n for which φ(n) is a permutation of n." |
71
Problem 71"Listing reduced proper fractions in ascending order of size." |
72
Problem 72"How many elements would be contained in the set of reduced proper fractions for d ≤ 1,000,000?" |
73
Problem 73"How many fractions lie between 1/3 and 1/2 in a sorted set of reduced proper fractions?" |
74
Problem 74"Determine the number of factorial chains that contain exactly sixty non-repeating terms." |
75
Problem 75"Find the number of different lengths of wire that can form a right angle triangle in only one way." |

76
Problem 76"How many different ways can one hundred be written as a sum of at least two positive integers?" |
77
Problem 77"What is the first value which can be written as the sum of primes in over five thousand different ways?" |
78
Problem 78"Investigating the number of ways in which coins can be separated into piles." |
79
Problem 79"By analysing a user's login attempts, can you determine the secret numeric passcode?" |
80
Problem 80"Calculating the digital sum of the decimal digits of irrational square roots." |
81
Problem 81"Find the minimal path sum from the top left to the bottom right by moving right and down." |
82
Problem 82"Find the minimal path sum from the left column to the right column." |
83
Problem 83"Find the minimal path sum from the top left to the bottom right by moving left, right, up, and down." |
84
Problem 84"In the game, Monopoly, find the three most popular squares when using two 4-sided dice." |
85
Problem 85"Investigating the number of rectangles in a rectangular grid." |
86
Problem 86"Exploring the shortest path from one corner of a cuboid to another." |
87
Problem 87"Investigating numbers that can be expressed as the sum of a prime square, cube, and fourth power?" |
88
Problem 88"Exploring minimal product-sum numbers for sets of different sizes." |
89
Problem 89"Develop a method to express Roman numerals in minimal form." |
90
Problem 90"An unexpected way of using two cubes to make a square." |
91
Problem 91"Find the number of right angle triangles in the quadrant." |
92
Problem 92"Investigating a square digits number chain with a surprising property." |
93
Problem 93"Using four distinct digits and the rules of arithmetic, find the longest sequence of target numbers." |
94
Problem 94"Investigating almost equilateral triangles with integral sides and area." |
95
Problem 95"Find the smallest member of the longest amicable chain with no element exceeding one million." |
96
Problem 96"Devise an algorithm for solving Su Doku puzzles." |
97
Problem 97"Find the last ten digits of the non-Mersenne prime: 28433 × 2 ^{7830457} + 1." |
98
Problem 98"Investigating words, and their anagrams, which can represent square numbers." |
99
Problem 99"Which base/exponent pair in the file has the greatest numerical value?" |
100
Problem 100"Finding the number of blue discs for which there is 50% chance of taking two blue." |

101
Problem 101"Investigate the optimum polynomial function to model the first k terms of a given sequence." |
102
Problem 102"For how many triangles in the text file does the interior contain the origin?" |
103
Problem 103"Investigating sets with a special subset sum property." |
104
Problem 104"Finding Fibonacci numbers for which the first and last nine digits are pandigital." |
105
Problem 105"Find the sum of the special sum sets in the file." |
106
Problem 106"Find the minimum number of comparisons needed to identify special sum sets." |
107
Problem 107"Determining the most efficient way to connect the network." |
108
Problem 108"Solving the Diophantine equation 1/ x + 1/y = 1/n." |
109
Problem 109"How many distinct ways can a player checkout in the game of darts with a score of less than 100?" |
110
Problem 110"Find an efficient algorithm to analyse the number of solutions of the equation 1/ x + 1/y = 1/n." |
111
Problem 111"Search for 10-digit primes containing the maximum number of repeated digits." |
112
Problem 112"Investigating the density of "bouncy" numbers." |
113
Problem 113"How many numbers below a googol (10 ^{100}) are not "bouncy"?" |
114
Problem 114"Investigating the number of ways to fill a row with separated blocks that are at least three units long." |
115
Problem 115"Finding a generalisation for the number of ways to fill a row with separated blocks." |
116
Problem 116"Investigating the number of ways of replacing square tiles with one of three coloured tiles." |
117
Problem 117"Investigating the number of ways of tiling a row using different-sized tiles." |
118
Problem 118"Exploring the number of ways in which sets containing prime elements can be made." |
119
Problem 119"Investigating the numbers which are equal to sum of their digits raised to some power." |
120
Problem 120"Finding the maximum remainder when ( a − 1)^{n} + (a + 1)^{n} is divided by a^{2}." |
121
Problem 121"Investigate the game of chance involving coloured discs." |
122
Problem 122"Finding the most efficient exponentiation method." |
123
Problem 123"Determining the remainder when ( p − 1)_{n}^{n} + (p + 1)_{n}^{n} is divided by p_{n}^{2}." |
124
Problem 124"Determining the k^{th} element of the sorted radical function." |
125
Problem 125"Finding square sums that are palindromic." |

126
Problem 126"Exploring the number of cubes required to cover every visible face on a cuboid." |
127
Problem 127"Investigating the number of abc-hits below a given limit." |
128
Problem 128"Which tiles in the hexagonal arrangement have prime differences with neighbours?" |
129
Problem 129"Investigating minimal repunits that divide by n." |
130
Problem 130"Finding composite values, n, for which n−1 is divisible by the length of the smallest repunits that divide it." |
131
Problem 131"Determining primes, p, for which n^{3} + n^{2}p is a perfect cube." |
132
Problem 132"Determining the first forty prime factors of a very large repunit." |
133
Problem 133"Investigating which primes will never divide a repunit containing 10 ^{n} digits." |
134
Problem 134"Finding the smallest positive integer related to any pair of consecutive primes." |
135
Problem 135"Determining the number of solutions of the equation x^{2} − y^{2} − z^{2} = n." |
136
Problem 136"Discover when the equation x^{2} − y^{2} − z^{2} = n has a unique solution." |
137
Problem 137"Determining the value of infinite polynomial series for which the coefficients are Fibonacci numbers." |
138
Problem 138"Investigating isosceles triangle for which the height and base length differ by one." |
139
Problem 139"Finding Pythagorean triangles which allow the square on the hypotenuse to be tiled." |
140
Problem 140"Investigating the value of infinite polynomial series for which the coefficients are a linear second order recurrence relation." |
141
Problem 141"Investigating progressive numbers, n, which are also square." |
142
Problem 142"Perfect Square Collection" |
143
Problem 143"Investigating the Torricelli point of a triangle " |
144
Problem 144"Investigating multiple reflections of a laser beam. " |
145
Problem 145"How many reversible numbers are there below one-billion?" |
146
Problem 146"Investigating a Prime Pattern " |
147
Problem 147"Rectangles in cross-hatched grids" |
148
Problem 148"Exploring Pascal's triangle." |
149
Problem 149"Searching for a maximum-sum subsequence." |
150
Problem 150"Searching a triangular array for a sub-triangle having minimum-sum." |

151
Problem 151"Paper sheets of standard sizes: an expected-value problem." |
152
Problem 152"Writing 1/2 as a sum of inverse squares" |
153
Problem 153"Investigating Gaussian Integers" |
154
Problem 154"Exploring Pascal's pyramid." |
155
Problem 155"Counting Capacitor Circuits." |
156
Problem 156"Counting Digits" |
157
Problem 157"Solving the diophantine equation ^{1}/_{a}+^{1}/_{b}= ^{p}/_{10n} " |
158
Problem 158"Exploring strings for which only one character comes lexicographically after its neighbour to the left." |
159
Problem 159"Digital root sums of factorisations." |
160
Problem 160"Factorial trailing digits" |
161
Problem 161"Triominoes" |
162
Problem 162"Hexadecimal numbers" |
163
Problem 163"Cross-hatched triangles" |
164
Problem 164"Numbers for which no three consecutive digits have a sum greater than a given value." |
165
Problem 165"Intersections" |
166
Problem 166"Criss Cross" |
167
Problem 167"Investigating Ulam sequences" |
168
Problem 168"Number Rotations" |
169
Problem 169"Exploring the number of different ways a number can be expressed as a sum of powers of 2." |
170
Problem 170"Find the largest 0 to 9 pandigital that can be formed by concatenating products." |
171
Problem 171"Finding numbers for which the sum of the squares of the digits is a square." |
172
Problem 172"Investigating numbers with few repeated digits." |
173
Problem 173"Using up to one million tiles how many different "hollow" square laminae can be formed?" |
174
Problem 174"Counting the number of "hollow" square laminae that can form one, two, three, ... distinct arrangements." |
175
Problem 175"Fractions involving the number of different ways a number can be expressed as a sum of powers of 2. " |

176
Problem 176"Rectangular triangles that share a cathetus." |
177
Problem 177"Integer angled Quadrilaterals." |
178
Problem 178"Step Numbers" |
179
Problem 179"Consecutive positive divisors" |
180
Problem 180"Rational zeros of a function of three variables." |
181
Problem 181"Investigating in how many ways objects of two different colours can be grouped." |
182
Problem 182"RSA encryption" |
183
Problem 183"Maximum product of parts" |
184
Problem 184"Triangles containing the origin." |
185
Problem 185"Number Mind" |
186
Problem 186"Connectedness of a network." |
187
Problem 187"Semiprimes" |
188
Problem 188"The hyperexponentiation of a number" |
189
Problem 189"Tri-colouring a triangular grid" |
190
Problem 190"Maximising a weighted product" |
191
Problem 191"Prize Strings" |
192
Problem 192"Best Approximations" |
193
Problem 193"Squarefree Numbers" |
194
Problem 194"Coloured Configurations" |
195
Problem 195 "Inscribed circles of triangles with one angle of 60 degrees" |
196
Problem 196 "Prime triplets" |
197
Problem 197"Investigating the behaviour of a recursively defined sequence" |
198
Problem 198"Ambiguous Numbers" |
199
Problem 199"Iterative Circle Packing" |
200
Problem 200"Find the 200th prime-proof sqube containing the contiguous sub-string "200"" |

201
Problem 201"Subsets with a unique sum" |
202
Problem 202"Laserbeam" |
203
Problem 203"Squarefree Binomial Coefficients" |
204
Problem 204"Generalised Hamming Numbers" |
205
Problem 205"Dice Game" |
206
Problem 206"Concealed Square" |
207
Problem 207"Integer partition equations" |
208
Problem 208"Robot Walks" |
209
Problem 209"Circular Logic" |
210
Problem 210"Obtuse Angled Triangles" |
211
Problem 211"Divisor Square Sum" |
212
Problem 212"Combined Volume of Cuboids" |
213
Problem 213"Flea Circus" |
214
Problem 214"Totient Chains" |
215
Problem 215"Crack-free Walls" |
216
Problem 216"Investigating the primality of numbers of the form 2 n^{2}-1" |
217
Problem 217"Balanced Numbers" |
218
Problem 218"Perfect right-angled triangles" |
219
Problem 219"Skew-cost coding" |
220
Problem 220"Heighway Dragon" |
221
Problem 221"Alexandrian Integers" |
222
Problem 222"Sphere Packing" |
223
Problem 223"Almost right-angled triangles I" |
224
Problem 224"Almost right-angled triangles II" |
225
Problem 225"Tribonacci non-divisors" |

226
Problem 226"A Scoop of Blancmange" |
227
Problem 227"The Chase" |
228
Problem 228"Minkowski Sums" |
229
Problem 229"Four Representations using Squares" |
230
Problem 230"Fibonacci Words" |
231
Problem 231"The prime factorisation of binomial coefficients" |
232
Problem 232"The Race" |
233
Problem 233"Lattice points on a circle" |
234
Problem 234"Semidivisible numbers" |
235
Problem 235"An Arithmetic Geometric sequence" |
236
Problem 236"Luxury Hampers" |
237
Problem 237"Tours on a 4 x n playing board" |
238
Problem 238"Infinite string tour" |
239
Problem 239"Twenty-two Foolish Primes" |
240
Problem 240"Top Dice" |
241
Problem 241"Perfection Quotients" |
242
Problem 242"Odd Triplets" |
243
Problem 243"Resilience" |
244
Problem 244"Sliders" |
245
Problem 245"Coresilience" |
246
Problem 246"Tangents to an ellipse" |
247
Problem 247"Squares under a hyperbola" |
248
Problem 248"Numbers for which Euler’s totient function equals 13!" |
249
Problem 249"Prime Subset Sums" |
250
Problem 250"250250" |

251
Problem 251"Cardano Triplets" |
252
Problem 252"Convex Holes" |
253
Problem 253"Tidying up" |
254
Problem 254"Sums of Digit Factorials" |
255
Problem 255"Rounded Square Roots" |
256
Problem 256"Tatami-Free Rooms" |
257
Problem 257"Angular Bisectors" |
258
Problem 258"A lagged Fibonacci sequence" |
259
Problem 259"Reachable Numbers" |
260
Problem 260"Stone Game" |
261
Problem 261"Pivotal Square Sums" |
262
Problem 262"Mountain Range." |
263
Problem 263"An engineers' dream come true" |
264
Problem 264"Triangle Centres" |
265
Problem 265"Binary Circles" |
266
Problem 266"Pseudo Square Root" |
267
Problem 267"Billionaire" |
268
Problem 268"Counting numbers with at least four distinct prime factors less than 100" |
269
Problem 269"Polynomials with at least one integer root" |
270
Problem 270"Cutting Squares" |
271
Problem 271"Modular Cubes, part 1" |
272
Problem 272"Modular Cubes, part 2" |
273
Problem 273"Sum of Squares" |
274
Problem 274"Divisibility Multipliers" |
275
Problem 275"Balanced Sculptures" |

276
Problem 276"Primitive Triangles" |
277
Problem 277"A Modified Collatz sequence" |
278
Problem 278"Linear Combinations of Semiprimes" |
279
Problem 279"Triangles with integral sides and an integral angle " |
280
Problem 280"Ant and seeds" |
281
Problem 281"Pizza Toppings" |
282
Problem 282"The Ackermann function" |
283
Problem 283"Integer sided triangles for which the area/perimeter ratio is integral." |
284
Problem 284"Steady Squares" |
285
Problem 285"Pythagorean odds" |
286
Problem 286"Scoring probabilities" |
287
Problem 287"Quadtree encoding (a simple compression algorithm)" |
288
Problem 288"An enormous factorial" |
289
Problem 289"Eulerian Cycles" |
290
Problem 290"Digital Signature" |
291
Problem 291"Panaitopol Primes" |
292
Problem 292"Pythagorean Polygons" |
293
Problem 293"Pseudo-Fortunate Numbers" |
294
Problem 294"Sum of digits - experience #23" |
295
Problem 295"Lenticular holes" |
296
Problem 296"Angular Bisector and Tangent" |
297
Problem 297"Zeckendorf Representation" |
298
Problem 298"Selective Amnesia" |
299
Problem 299"Three similar triangles" |
300
Problem 300"Protein folding" |

301
Problem 301"Nim" |
302
Problem 302"Strong Achilles Numbers" |
303
Problem 303"Multiples with small digits" |
304
Problem 304"Primonacci" |
305
Problem 305"Reflexive Position" |
306
Problem 306"Paper-strip Game" |
307
Problem 307"Chip Defects" |
308
Problem 308"An amazing Prime-generating Automaton" |
309
Problem 309"Integer Ladders" |
310
Problem 310"Nim Square" |
311
Problem 311"Biclinic Integral Quadrilaterals" |
312
Problem 312"Cyclic paths on Sierpiński graphs" |
313
Problem 313"Sliding game" |
314
Problem 314"The Mouse on the Moon" |
315
Problem 315"Digital root clocks" |
316
Problem 316"Numbers in decimal expansions" |
317
Problem 317"Firecracker" |
318
Problem 318"2011 nines" |
319
Problem 319"Bounded Sequences" |
320
Problem 320"Factorials divisible by a huge integer" |
321
Problem 321"Swapping Counters" |
322
Problem 322"Binomial coefficients divisible by 10" |
323
Problem 323"Bitwise-OR operations on random integers" |
324
Problem 324"Building a tower" |
325
Problem 325"Stone Game II" |

326
Problem 326"Modulo Summations" |
327
Problem 327"Rooms of Doom" |
328
Problem 328"Lowest-cost Search" |
329
Problem 329"Prime Frog" |
330
Problem 330"Euler's Number" |
331
Problem 331"Cross flips" |
332
Problem 332"Spherical triangles" |
333
Problem 333"Special partitions" |
334
Problem 334"Spilling the beans" |
335
Problem 335"Gathering the beans" |
336
Problem 336"Maximix Arrangements" |
337
Problem 337"Totient Stairstep Sequences" |
338
Problem 338"Cutting Rectangular Grid Paper" |
339
Problem 339"Peredur fab Efrawg" |
340
Problem 340"Crazy Function" |
341
Problem 341"Golomb's self-describing sequence" |
342
Problem 342"The totient of a square is a cube" |
343
Problem 343"Fractional Sequences" |
344
Problem 344"Silver dollar game" |
345
Problem 345"Matrix Sum" |
346
Problem 346"Strong Repunits" |
347
Problem 347"Largest integer divisible by two primes" |
348
Problem 348"Sum of a square and a cube" |
349
Problem 349"Langton's ant" |
350
Problem 350"Constraining the least greatest and the greatest least" |

351
Problem 351"Hexagonal orchards" |
352
Problem 352"Blood tests" |
353
Problem 353"Risky moon" |
354
Problem 354"Distances in a bee's honeycomb " |
355
Problem 355"Maximal coprime subset" |
356
Problem 356"Largest roots of cubic polynomials" |
357
Problem 357"Prime generating integers" |
358
Problem 358"Cyclic numbers" |
359
Problem 359"Hilbert's New Hotel" |
360
Problem 360"Scary Sphere" |
361
Problem 361"Subsequence of Thue-Morse sequence" |
362
Problem 362"Squarefree factors" |
363
Problem 363"Bézier Curves" |
364
Problem 364"Comfortable distance" |
365
Problem 365"A huge binomial coefficient" |
366
Problem 366"Stone Game III" |

### Levels Completed

125 |
150 |
175 |
200 |
225 |
250 | ||||

275 |
300 |
325 |

### Awards Earned

Centurion
Centurion Solve one hundred consecutive problems |
One In A Hundred
One In A Hundred Be among the first hundred to solve a problem |
Unlucky Squares
Unlucky Squares Solve thirteen square numbered problems |
Prime Obsession
Prime Obsession Solve fifty prime numbered problems |
Perfection
Perfection Solve every problem |
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On The Ball II
On The Ball II Solve the five most recent problems |
State Of The Art
State Of The Art Solve the most recent twenty-five problems |
Trinary Triumph
Trinary Triumph Solve problems 1, 3, 9, 27, 81, and 243 |
Fibonacci Fever
Fibonacci Fever Solve the first twelve Fibonacci numbered problems |
Triangle Trophy
Triangle Trophy Solve the first twenty-five triangle numbered problems |
Lucky Luke
Lucky Luke Solve fifty lucky numbered problems |
High Flyer
High Flyer Progress to the maximum level |
Gold Medal
Gold Medal The first to solve a problem |
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Déjà Vu
Déjà Vu
Solve ten pairs of related problems |