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Project Euler

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


Level 4

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 21000?"
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 ab for 2 ≤ 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 nth 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 11 + 22 + ... + 10001000."
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, ab, finding the maximum digital sum."
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 nth 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 100th convergent of the continued fraction for e."
66 Problem 66
"Investigate the Diophantine equation x2 − Dy2 = 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 × 27830457 + 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 (10100) 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 a2."
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 (pn − 1)n + (pn + 1)n is divided by pn2."
124 Problem 124
"Determining the kth 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 n3 + n2p 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 10n 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 x2y2z2 = n."
136 Problem 136
"Discover when the equation x2y2z2 = 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 2n2-1"
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

Decathlete
Solve ten consecutive problems
Centurion Centurion
Solve one hundred consecutive problems
As Easy As Pi
Solve problems 3, 14, 15, 92, 65, 35, 89, 79, 32, 38, and 46
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
Baby Steps
Solve three problems
The Journey Begins
Progress to Level 1 by solving twenty-five problems
Perfection Perfection
Solve every problem
Daring Dozen
Solve twelve problems with an ID containing three digits
On The Ball
Solve the most recent problem
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
Pythagorean Triplet
Solve three Pythagorean problems
Déjà Vu Déjà Vu
Solve ten pairs of related problems