Geometry Puzzle – Critical Thinking 20
How many three-digit numbers have digits that add to 7? It looks like a counting question, but it’s really a clean stars-and-bars problem with one restriction: the hundreds digit must be at least 1. Once you spot the structure, the answer falls out fast. Key takeaways: A three-digit number \( \overline{abc} \) has hundreds digit […]
Geometry Puzzle – Critical Thinking 19
If N and P are distinct primes, how many positive divisors does N^2 times P^4 have? The slick way: for any positive integer factored as p1^a * p2^b * … * pk^z, the divisor count is (a+1)(b+1)…(z+1). Plug in: (2+1)(4+1) = 15. Key takeaways: Divisor count formula: if \( n = p_1^{a_1} p_2^{a_2} \cdots p_k^{a_k} […]
