Deep within a forest canyon, Emek and Tara reached an ancient bridge whose stone sections displayed numerical codes. A weathered sign explained that only sections with the required divisibility properties would become stable. The visible codes included 144, 175, 198, 221, and 270, and the clues referred to divisibility by numbers such as 3, 5, 9, and 11. Emek and Tara analyzed each code, compared their divisibility relationships, and verified every choice before stepping forward. Their careful reasoning activated a safe path across the canyon, allowing them to reach the isolated research outpost with valuable supplies and scientific equipment.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
Test each code for divisibility by both numbers, not just one.
A bridge clue requires a code divisible by both 9 and 11. Which stone section should Emek and Tara choose?
144175198270Correct! 198 is divisible by both 9 and 11.
Check the digit sum for divisibility by 9, then test divisibility by 11.
Next🎉 Congrats! You got this question!
Hint
Test every code and count it once if it is divisible by at least one of the two numbers.
Among the bridge codes 144, 175, 198, 221, and 270, how many are divisible by 3 or 5?
Correct! Four of the codes are divisible by 3 or 5.
Use the digit-sum rule for 3 and the last-digit rule for 5.
Next🎉 Congrats! You got this question!
Hint
Check all four divisibility conditions for each code and count how many it satisfies.
The final clue asks for a code divisible by exactly one of the numbers 3, 5, 9, and 11. Which code satisfies the clue?
144175198270Correct! 175 is divisible by 5 but not by 3, 9, or 11.
Look for a code that satisfies one—and only one—of the four divisibility tests.
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🎉 Congrats! You finished this challenge set!
