Leading an expedition through an abandoned mining valley, Emek and Tara followed numbered trail markers left by earlier explorers. Their guidebook explained that genuine markers shared specific divisibility properties and common factors, while misleading markers did not. The numbered stones included values such as 168, 180, 187, 216, and 245. At each fork, they tested divisibility, identified common factors between key markers, and compared the resulting number patterns before choosing a direction. Their careful reasoning filtered out the false trails, and just before nightfall they reached the hidden supply cache, ensuring the expedition could continue safely the next day.

Challenges

Challenge 1 of 5

Challenges

Challenge 1 of 4
Hint
Use the digit-sum rule for divisibility by 9.
A student says, "The marker 216 is not divisible by 9 because it does not end in 9." Which statement correctly checks this claim?
The student is correct because multiples of 9 must end in 9.The student is incorrect because 2 + 1 + 6 = 9, so 216 is divisible by 9.The student is correct because 216 is only divisible by even numbers.The student is incorrect because every three-digit number is divisible by 9.
Correct! The digits of 216 add to 9, so 216 is divisible by 9.
A number does not need to end in 9 to be divisible by 9; check its digit sum.
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Hint
Prime-factorize both numbers or list their common factors.
Two genuine trail markers are numbered 168 and 180. What is their greatest common factor?
Correct! The greatest common factor of 168 and 180 is 12.
Find the largest factor that divides both 168 and 180 exactly.
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Hint
First test divisibility by 3, then find the greatest common factor with 168.
The guidebook says a genuine marker must be divisible by 3 and share a common factor greater than 10 with the marker 168. Which marker satisfies both conditions?
190187216245
Correct! 216 is divisible by 3, and its greatest common factor with 168 is 24.
Check both requirements: divisibility by 3 and a common factor with 168 greater than 10.
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Keşif Kodu Yolu
TR
ARC_G11_NUM_01_STORY_03
Keşif Kodu Yolu
Expedition Code Trail
EN
ARC_G11_NUM_01_STORY_03
Expedition Code Trail