Challenges · Examples

Solve Examples

Unlock challenges step by step. Every solved example adds XP to your career.

0 / 298 solved

268 results

#271 · Combinatorics

Onto functions from {1,…,5} to {1,2,3}

Locked
D9/10405XP

#272 · Functions

Solutions of f(f(x)) = x for f(x) = x² − 2

Locked
D9/10405XP

#273 · Calculus

Series ∑ n²/2ⁿ

Locked
D9/10405XP

#274 · Arithmetic

Largest n such that (n + 10) divides n³ + 100

Locked
D10/10500XP

#275 · Algebra

x⁴ + y⁴ + z⁴ from elementary symmetric polynomials

Locked
D10/10500XP

#276 · Combinatorics

10-digit binary strings with no two consecutive 1s

Locked
D10/10500XP

#277 · Calculus

Series ∑ k/2^k

Locked
D10/10500XP

#278 · Algebra

Sum of integers n with |n² − 10n| < 5

Locked
D10/10500XP

#279 · Combinatorics

5-element subsets of {1, …, 20} with no two consecutive elements

Locked
D10/10500XP

#280 · Arithmetic

GCD of 1! + 2! + … + 10! and 10!

Locked
D10/10500XP

#281 · Functions

Real solutions of x² = 2^x

Locked
D10/10500XP

#282 · Combinatorics

Non-negative 4-tuples summing to 10 with a + b ≥ 3

Locked
D10/10500XP

#283 · Arithmetic

(1⁵ + 2⁵ + … + 100⁵) mod 4

Locked
D10/10500XP

#284 · Arithmetic

(∑_{k=1}^{100} k · k!) mod 100

Locked
D10/10500XP

#285 · Arithmetic

Sum of n where n² + 3n + 5 is a prime dividing n² + 1

Locked
D10/10500XP

#286 · Equations

Ordered pairs (x, y) with 1/x + 1/y = 1/12

Locked
D10/10500XP

#287 · Arithmetic

Sum of n ≤ 1000 with φ(n) = n/2

Locked
D10/10500XP

#288 · Combinatorics

Positive integer solutions of x + 2y + 3z = 30

Locked
D10/10500XP

#289 · Calculus

Series ∑ k(k+1)/2^k

Locked
D10/10500XP

#290 · Combinatorics

Tiling a 1 × 6 strip with red, blue, and white tiles

Locked
D10/10500XP

#291 · Algebra

Maximum of x²y³z given x + y + z = 1

Locked
D10/10500XP

#292 · Arithmetic

Largest prime factor of 101,010,101

Locked
D10/10500XP

#293 · Combinatorics

Vandermonde sum C(10,0)² + C(10,1)² + … + C(10,10)²

Locked
D10/10500XP

#294 · Combinatorics

Lattice paths from (0,0) to (10,10) passing through (5,5)

Locked
D10/10500XP

#295 · Arithmetic

Product of 4 consecutive integers – largest guaranteed divisor

Locked
D10/10500XP

#296 · Arithmetic

Wieferich primes up to 20

Locked
D10/10500XP

#297 · Calculus

Maximum area of rectangle inscribed in right triangle with legs 3 and 4

Locked
D10/10500XP

#298 · Arithmetic

Primes appearing in twin prime pairs up to 100

Locked
D10/10500XP