مرحله ۳ • لیست سوالات

لیست سوالات

1 - مضرب‌های ۳ و ۵

2 - عددهای فیبوناچی زوج

3 - بزرگترین عامل اول

4 - بزرگترین حاصل‌ضرب متقارن

5 - کوچکترین مضرب

6 - اختلاف جمع مربع‌ها

7 - 10001 امین عدد اول

8 - بزرگترین حاصل ضرب در دنباله

9 - سه‌گانه‌ی فیثاغورسی خاص

10 - مجموع اعداد اول

11 - بیش‌ترین حاصل‌ضرب در یک جدول

12 - عدد مثلثی خیلی تقسیم پذیر

13 - جمع بزرگ

14 - بزرگترین توالی کولاتز

15 - مسیر روی توری

16 - جمع ارقام توانی

17 - شمارش حروف اعداد

18 - بیشترین جمع در مسیر ۱

19 - شمارش یک‌شنبه‌ها

20 - جمع ارقام فاکتوریلی

21 - اعداد دوست داشتنی

22 - امتیاز نام‌ها

23 - مجموع نا‌زائد‌ها

24 - جایگشت‌های لغت‌نامه‌ای

25 - عدد فیبوناچی 1000 رقمی

26 - چرخه‌های متناظر

27 - اعداد اول درجه دو‌یی

28 - عدد قطرهای مارپیچ

29 - توان‌های متمایز

30 - توان پنجم ارقام

31 - مجموع سکه‌ها

32 - ضرب پان‌رقمی‌ها

33 - خط‌زدن رقم در کسرها

34 - فاکتوریل ارقام

35 - اعداد اول چرخشی

36 - اعداد متقارن در دو مبنا

37 - اعداد اول برش‌پذیر

38 - مضرب‌های پان‌رقمی

39 - مثلث‌های قائم الزاوایه‌ی صحیح

40 - ثابت چمپرنون

41 - عدد اول پان‌رقمی

42 - اعداد مثلثی کد شده

43 - بخش‌پذیری زیررشته

44 - اعداد پنج‌ضلعی‌

45 - مثلثی، پنج‌ضلعی و شش‌ضلعی

46 - حدس دیگر گلدباخ

47 - عوامل اول متفاوت

48 - به توان رساندن خود عدد

49 - جایگشت‌های اول

50 - جمع اعداد اول متوالی

51 - تغییر ارقام عدد اول

52 - مضرب‌های جایگشتی

53 - انتخاب‌های ترکیبیاتی

54 - Poker hands

55 - اعداد لیکرل

56 - جمع ارقام قدرتمند

57 - همگرایی ریشه دوم

58 - اعداد اول مارپیچی

59 - رمزگذاری xor

60 - مجوعه‌های جفت اول

61 - Cyclical figurate numbers

62 - جایگشت‌های مکعب کامل

63 - تعداد ارقام توان

64 - ریشه‌ها با دوره تناوب فرد

65 - Convergents of e

66 - Diophantine equation

67 - Maximum path sum II

68 - Magic 5-gon ring

69 - Totient maximum

70 - Totient permutation

71 - Ordered fractions

72 - Counting fractions

73 - Counting fractions in a range

74 - Digit factorial chains

75 - Singular integer right triangles

76 - شمارش مجموع‌ها

77 - Prime summations

78 - Coin partitions

79 - Passcode derivation

80 - Square root digital expansion

81 - Path sum: two ways

82 - Path sum: three ways

83 - Path sum: four ways

84 - Monopoly odds

85 - Counting rectangles

86 - Cuboid route

87 - Prime power triples

88 - Product-sum numbers

89 - Roman numerals

90 - Cube digit pairs

91 - Right triangles with integer coordinates

92 - Square digit chains

93 - Arithmetic expressions

94 - Almost equilateral triangles

95 - Amicable chains

96 - Su Doku

97 - Large non-Mersenne prime

98 - Anagramic squares

99 - Largest exponential

100 - Arranged probability

101 - Optimum polynomial

102 - Triangle containment

103 - Special subset sums: optimum

104 - Pandigital Fibonacci ends

105 - Special subset sums: testing

106 - Special subset sums: meta-testing

107 - Minimal network

108 - Diophantine reciprocals I

109 - Darts

110 - Diophantine reciprocals II

111 - Primes with runs

112 - Bouncy numbers

113 - Non-bouncy numbers

114 - Counting block combinations I

115 - Counting block combinations II

116 - Red, green or blue tiles

117 - Red, green, and blue tiles

118 - Pandigital prime sets

119 - Digit power sum

120 - Square remainders

121 - Disc game prize fund

122 - Efficient exponentiation

123 - Prime square remainders

124 - Ordered radicals

125 - Palindromic sums

126 - Cuboid layers

127 - abc-hits

128 - Hexagonal tile differences

129 - Repunit divisibility

130 - Composites with prime repunit property

131 - Prime cube partnership

132 - Large repunit factors

133 - Repunit nonfactors

134 - Prime pair connection

135 - Same differences

136 - Singleton difference

137 - Fibonacci golden nuggets

138 - Special isosceles triangles

139 - Pythagorean tiles

140 - Modified Fibonacci golden nuggets

141 - Investigating progressive numbers, n, which are also square

142 - Perfect Square Collection

143 - Investigating the Torricelli point of a triangle

144 - Investigating multiple reflections of a laser beam

145 - How many reversible numbers are there below one-billion?

146 - Investigating a Prime Pattern

147 - Rectangles in cross-hatched grids

148 - Exploring Pascal's triangle

149 - Searching for a maximum-sum subsequence

150 - Searching a triangular array for a sub-triangle having minimum-sum

151 - Paper sheets of standard sizes: an expected-value problem

152 - Writing 1/2 as a sum of inverse squares

153 - Investigating Gaussian Integers

154 - Exploring Pascal's pyramid

154 - Exploring Pascal's pyramid

155 - Counting Capacitor Circuits

156 - Counting Digits

157 - Solving the diophantine equation ¹/_a+¹/_b= ^p/_10ⁿ

158 - Exploring strings for which only one character comes lexicographically after its neighbour to the left

159 - Digital root sums of factorisations

160 - Factorial trailing digits

161 - Triominoes

162 - Hexadecimal numbers

163 - Cross-hatched triangles

164 - Numbers for which no three consecutive digits have a sum greater than a given value

165 - Intersections

166 - Criss Cross

167 - Investigating Ulam sequences

168 - Number Rotations

169 - Exploring the number of different ways a number can be expressed as a sum of powers of 2

170 - Find the largest 0 to 9 pandigital that can be formed by concatenating products

171 - Finding numbers for which the sum of the squares of the digits is a square

172 - Investigating numbers with few repeated digits

173 - Using up to one million tiles how many different "hollow" square laminae can be formed?

174 - Counting the number of "hollow" square laminae that can form one, two, three, ... distinct arrangements

175 - Fractions involving the number of different ways a number can be expressed as a sum of powers of 2

176 - Right-angled triangles that share a cathetus

177 - Integer angled Quadrilaterals

178 - Step Numbers

179 - Consecutive positive divisors

180 - Rational zeros of a function of three variables

181 - Investigating in how many ways objects of two different colours can be grouped

182 - RSA encryption

183 - Maximum product of parts

184 - Triangles containing the origin

185 - Number Mind

186 - Connectedness of a network

187 - Semiprimes

188 - The hyperexponentiation of a number

189 - Tri-colouring a triangular grid

190 - Maximising a weighted product

191 - Prize Strings

192 - Best Approximations

193 - Squarefree Numbers

194 - Coloured Configurations

195 - Inscribed circles of triangles with one angle of 60 degrees

196 - Prime triplets

197 - Investigating the behaviour of a recursively defined sequence

198 - Ambiguous Numbers

199 - Iterative Circle Packing

200 - Find the 200th prime-proof sqube containing the contiguous sub-string "200"

201 - Subsets with a unique sum

202 - Laserbeam

203 - Squarefree Binomial Coefficients

204 - Generalised Hamming Numbers

205 - Dice Game

206 - Concealed Square

207 - Integer partition equations

208 - Robot Walks

209 - Circular Logic

210 - Obtuse Angled Triangles

211 - Divisor Square Sum

212 - Combined Volume of Cuboids

213 - Flea Circus

214 - Totient Chains

215 - Crack-free Walls

216 - Investigating the primality of numbers of the form 2n²-1

217 - Balanced Numbers

218 - Perfect right-angled triangles

219 - Skew-cost coding

220 - Heighway Dragon

221 - Alexandrian Integers

222 - Sphere Packing

223 - Almost right-angled triangles I

224 - Almost right-angled triangles II

225 - Tribonacci non-divisors

226 - A Scoop of Blancmange

227 - The Chase

228 - Minkowski Sums

229 - Four Representations using Squares

230 - Fibonacci Words

231 - The prime factorisation of binomial coefficients

232 - The Race

233 - Lattice points on a circle

234 - Semidivisible numbers

235 - An Arithmetic Geometric sequence

236 - Luxury Hampers

237 - Tours on a 4 x n playing board

238 - Infinite string tour

239 - Twenty-two Foolish Primes

240 - Top Dice

241 - Perfection Quotients

242 - Odd Triplets

243 - Resilience

244 - Sliders

245 - Coresilience

246 - Tangents to an ellipse

247 - Squares under a hyperbola

248 - Numbers for which Euler’s totient function equals 13!

249 - Prime Subset Sums

250 - 250250

251 - Cardano Triplets

252 - Convex Holes

253 - Tidying up

254 - Sums of Digit Factorials

255 - Rounded Square Roots

256 - Tatami-Free Rooms

257 - Angular Bisectors

258 - A lagged Fibonacci sequence

259 - Reachable Numbers

260 - Stone Game

261 - Pivotal Square Sums

262 - Mountain Range

263 - An engineers' dream come true

264 - Triangle Centres

265 - Binary Circles

266 - Pseudo Square Root

267 - Billionaire

268 - Counting numbers with at least four distinct prime factors less than 100

269 - Polynomials with at least one integer root

270 - Cutting Squares

271 - Modular Cubes, part 1

272 - Modular Cubes, part 2

273 - Sum of Squares

274 - Divisibility Multipliers

275 - Balanced Sculptures

276 - Primitive Triangles

277 - A Modified Collatz sequence

278 - Linear Combinations of Semiprimes

279 - Triangles with integral sides and an integral angle

279 - Triangles with integral sides and an integral angle

280 - Ant and seeds

281 - Pizza Toppings

282 - The Ackermann function

283 - Integer sided triangles for which the area/perimeter ratio is integral

284 - Steady Squares

285 - Pythagorean odds

286 - Scoring probabilities

287 - Quadtree encoding (a simple compression algorithm)

287 - Quadtree encoding (a simple compression algorithm)

288 - An enormous factorial

289 - Eulerian Cycles

290 - Digital Signature

291 - Panaitopol Primes

292 - Pythagorean Polygons

293 - Pseudo-Fortunate Numbers

294 - Sum of digits - experience #23

295 - Lenticular holes

296 - Angular Bisector and Tangent

297 - Zeckendorf Representation

298 - Selective Amnesia

299 - Three similar triangles

300 - Protein folding

302 - Strong Achilles Numbers

303 - Multiples with small digits

304 - Primonacci

305 - Reflexive Position

306 - Paper-strip Game

307 - Chip Defects

308 - An amazing Prime-generating Automaton

309 - Integer Ladders

310 - Nim Square

311 - Biclinic Integral Quadrilaterals

312 - Cyclic paths on Sierpiński graphs

313 - Sliding game

314 - The Mouse on the Moon

315 - Digital root clocks

316 - Numbers in decimal expansions

317 - Firecracker

318 - 2011 nines

319 - Bounded Sequences

320 - Factorials divisible by a huge integer

321 - Swapping Counters

322 - Binomial coefficients divisible by 10

323 - Bitwise-OR operations on random integers

324 - Building a tower

325 - Stone Game II

326 - Modulo Summations

327 - Rooms of Doom

328 - Lowest-cost Search

329 - Prime Frog

330 - Euler's Number

331 - Cross flips

332 - Spherical triangles

333 - Special partitions

334 - Spilling the beans

335 - Gathering the beans

336 - Maximix Arrangements

337 - Totient Stairstep Sequences

338 - Cutting Rectangular Grid Paper

339 - Peredur fab Efrawg

340 - Crazy Function

341 - Golomb's self-describing sequence

342 - The totient of a square is a cube

343 - Fractional Sequences

344 - Silver dollar game

345 - Matrix Sum

346 - Strong Repunits

347 - Largest integer divisible by two primes

348 - Sum of a square and a cube

349 - Langton's ant

350 - Constraining the least greatest and the greatest least

351 - Hexagonal orchards

352 - Blood tests

353 - Risky moon

354 - Distances in a bee's honeycomb

355 - Maximal coprime subset

356 - Largest roots of cubic polynomials

357 - Prime generating integers

358 - Cyclic numbers

359 - Hilbert's New Hotel

360 - Scary Sphere

361 - Subsequence of Thue-Morse sequence

362 - Squarefree factors

363 - Bézier Curves

364 - Comfortable distance

365 - A huge binomial coefficient

366 - Stone Game III

367 - Bozo sort

368 - A Kempner-like series

369 - Badugi

370 - Geometric triangles

371 - Licence plates

372 - Pencils of rays

373 - Circumscribed Circles

374 - Maximum Integer Partition Product

375 - Minimum of subsequences

376 - Nontransitive sets of dice

377 - Sum of digits, experience 13

378 - Triangle Triples

379 - Least common multiple count

380 - Amazing Mazes!

381 - (prime-k) factorial

382 - Generating polygons

383 - Divisibility comparison between factorials

384 - Rudin-Shapiro sequence

385 - Ellipses inside triangles

386 - Maximum length of an antichain

387 - Harshad Numbers

388 - Distinct Lines

389 - Platonic Dice

390 - Triangles with non rational sides and integral area

391 - Hopping Game

392 - Enmeshed unit circle

393 - Migrating ants

394 - Eating pie

395 - Pythagorean tree

396 - Weak Goodstein sequence

397 - Triangle on parabola

398 - Cutting rope

399 - Squarefree Fibonacci Numbers

400 - Fibonacci tree game

401 - Sum of squares of divisors

402 - Integer-valued polynomials

403 - Lattice points enclosed by parabola and line

404 - Crisscross Ellipses

405 - A rectangular tiling

406 - Guessing Game

407 - Idempotents

408 - Admissible paths through a grid

409 - Nim Extreme

410 - Circle and tangent line

411 - Uphill paths

412 - Gnomon numbering

413 - One-child Numbers

414 - Kaprekar constant

415 - Titanic sets

416 - A frog's trip

417 - Reciprocal cycles II

418 - Factorisation triples

419 - Look and say sequence

420 - 2x2 positive integer matrix

421 - Prime factors of n¹⁵+1

422 - Sequence of points on a hyperbola

423 - Consecutive die throws

424 - Kakuro

425 - Prime connection

426 - Box-ball system

427 - n-sequences

428 - Necklace of circles

429 - Sum of squares of unitary divisors

430 - Range flips

431 - Square Space Silo

432 - Totient sum

433 - Steps in Euclid's algorithm

434 - Rigid graphs

435 - Polynomials of Fibonacci numbers

436 - Unfair wager

437 - Fibonacci primitive roots

438 - Integer part of polynomial equation's solutions

439 - Sum of sum of divisors

440 - GCD and Tiling

441 - The inverse summation of coprime couples

442 - Eleven-free integers

443 - GCD sequence

444 - The Roundtable Lottery

445 - Retractions A

446 - Retractions B

447 - Retractions C

448 - Average least common multiple

449 - Chocolate covered candy

450 - Hypocycloid and Lattice points

451 - Modular inverses

452 - Long Products

453 - Lattice Quadrilaterals

454 - Diophantine reciprocals III

455 - Powers With Trailing Digits

456 - Triangles containing the origin II

457 - A polynomial modulo the square of a prime

458 - Permutations of Project

459 - Flipping game

460 - An ant on the move

461 - Almost Pi

462 - Permutation of 3-smooth numbers

463 - A weird recurrence relation

464 - Möbius function and intervals

465 - Polar polygons

466 - Distinct terms in a multiplication table

467 - Superinteger

468 - Smooth divisors of binomial coefficients

469 - Empty chairs

470 - Super Ramvok

471 - Triangle inscribed in ellipse

472 - Comfortable Distance II

473 - Phigital number base

474 - Last digits of divisors

475 - Music festival

476 - Circle Packing II

477 - Number Sequence Game

478 - Mixtures

479 - Roots on the Rise

480 - The Last Question

481 - Chef Showdown

482 - The incenter of a triangle

483 - Repeated permutation

484 - Arithmetic Derivative

485 - Maximum number of divisors

486 - Palindrome-containing strings

487 - Sums of power sums

488 - Unbalanced Nim

489 - Common factors between two sequences

490 - Jumping frog

491 - Double pandigital number divisible by 11

492 - Exploding sequence

493 - Under The Rainbow

494 - Collatz prefix families

495 - Writing n as the product of k distinct positive integers

496 - Incenter and circumcenter of triangle

497 - Drunken Tower of Hanoi

498 - Remainder of polynomial division

499 - St. Petersburg Lottery

500 - Problem 500!!!

501 - Eight Divisors

502 - Counting Castles

503 - Compromise or persist

504 - Square on the Inside

505 - Bidirectional Recurrence

506 - Clock sequence

507 - Shortest Lattice Vector

508 - Integers in base i-1

509 - Divisor Nim

510 - Tangent Circles

511 - Sequences with nice divisibility properties

512 - Sums of totients of powers

513 - Integral median

514 - Geoboard Shapes

515 - Dissonant Numbers

516 - 5-smooth totients