MathGrit
ProblemsTechniquesPricing
Sign inGet started
Back to problems

Concatenating Five 5s Distinct Products

1800SpecialistCombinatoricsCounting Principles

13th Annual Harvard-MIT Mathematics Tournament

How many different numbers are obtainable from five 5s by first concatenating some of the 5s, then multiplying them together? For example, we could do $5 \cdot 55 \cdot 55,555 \cdot 55$, or $55555$, but not $5 \cdot 5$ or $2525$.
0 students attempted0% solvedRating 1800

Related practice paths

AIME PracticeInteger-answer practice for deeper multi-step problems.How to Qualify for AIMEScore goals, contest choice, and prep habits for AIME hopefuls.AIME Practice StrategyHow to improve accuracy on high-difficulty problems.

Ready to check your answer?

Create an account to submit answers, save history, and track your rating.

Progressive Hints

Unlock hints one at a time — each reveals a little more without spoiling the solution.

Step-by-Step Solutions1

Multiple solution approaches with detailed walkthroughs, unlocked after you solve the problem.

AI-Powered Grading

Instant feedback on your answer — handles fractions, decimals, and equivalent forms.

Curated problem bank

Supported tracks for AMC, AIME, MATHCOUNTS, and olympiad-style training, plus global problem sources like UKMT, Euclid, and Kangaroo.