Challenge 1: The Curious Frog

Our beloved Froge is hopping along a path, following a peculiar pattern: 1 hop forward, 2 hops back, 3 hops forward, 4 hops back, and so on. If Froge starts at position 0, where will Froge be after completing the 7-hop cycle?

Can you determine a general pattern? Share your insights!

Challenge 2: Numeric Labyrinth

Froge has discovered a numeric labyrinth! Each number in a sequence represents a step count to the next number, starting from 2. The sequence goes 2, 4, 5, 7, 10, 14... Can you identify the pattern and predict the 10th number in this series?

Join the discussion on our Numeric Labyrinth Forum.

Challenge 3: Perfect Patterns

Investigate the perfect number sequence. A number is called 'perfect' if it is equal to the sum of its positive divisors, excluding itself. For example, 6 is a perfect number because 1 + 2 + 3 = 6. What other perfect numbers exist below 500?

Submit your findings! Perhaps discover a new perfect number?