Exercises · T04 number problems

Covers: classic number algorithms — divisibility, digit tricks, series, number-theory-lite, numeric reasoning combining loops and conditions. Lectures L09–L11 (builds on loops/conditions; feeds search/sort fluency). Outcomes PF-5.2–PF-5.4, PF-6.x.

11 exercises · ladder 🟢 → 🔴. Distinct from T03: these are algorithmic tasks about numbers; T03 tasks were about loop mechanics themselves.

PF-E-043 · Even/Odd Reporter (range)

Difficulty: Beginner · Lecture: L09 · Outcomes: PF-5.1, PF-4.1 Prerequisites: E-027, E-016 Problem: Read two integers lo ≤ hi (−50 to 50). Print each number in the range labeled even or odd, all on one line, space-separated. Input: two integers · Output: one line of labeled numbers. Sample: 3 6 → 3 odd 4 even 5 odd 6 even Hints: % 2 inside the loop; negative numbers: -3 % 2 is -1 in C++ — handle it.

PF-E-044 · Multiples Counter

Difficulty: Beginner · Lecture: L09 · Outcomes: PF-5.2, PF-4.1 Prerequisites: E-043 Problem: Read k (2–9) and n (1–1000). Count how many integers in 1..n are divisible by k, and print their sum. Input: two integers · Output: count and sum. Sample: 3 10 → count: 3 / sum: 18 Hints: i % k == 0 — accumulate two things in one loop.

PF-E-045 · Perfect Number Check

Difficulty: Foundational · Lecture: L10 · Outcomes: PF-5.3 Prerequisites: E-044, E-039 Problem: Read n (1–10,000). A number is perfect if it equals the sum of its proper divisors. Print perfect or not perfect, then list the divisors found. Input: one integer · Output: verdict + divisor list. Sample: 28 → perfect (1 2 4 7 14) Hints: loop divisors to √n in pairs (i and n/i) to keep it fast.

PF-E-046 · GCD (Euclid, iterative)

Difficulty: Foundational · Lecture: L10 · Outcomes: PF-5.3 Prerequisites: E-045 Problem: Read two positive integers; compute their GCD with the Euclidean algorithm (while loop, %), and print the GCD and the number of reduction steps. Input: two integers · Output: GCD + steps. Sample: 48 36 → gcd: 12 / steps: 3 Hints: while (b != 0) { t = b; b = a % b; a = t; } — trace once by hand.

PF-E-047 · Armstrong Numbers (range)

Difficulty: Foundational · Lecture: L10 · Outcomes: PF-5.3 Prerequisites: E-032 Problem: Print all Armstrong numbers (a number equal to the sum of its digits each raised to the digit-count power) between 1 and 999, one per line, with their digit decomposition in parentheses. Input: none · Output: the list. Sample: 153 (1^3 + 5^3 + 3^3) is among the lines. Hints: nest the digit-extraction loop inside the range loop; digit count varies per number.

PF-E-048 · Binary Representation

Difficulty: Intermediate · Lecture: L10 · Outcomes: PF-5.3 Prerequisites: E-033, E-047 Problem: Read a non-negative integer (< 2³¹); print its binary representation (no leading zeros; 0 prints as 0). Build it with % 2 / / 2 arithmetic only — no bitset. Input: one integer · Output: one binary string. Sample: 13 → 1101 Hints: remainders come out reversed — reuse the reversal idea or collect then reverse.

PF-E-049 · Prime Twins Gap Report

Difficulty: Intermediate · Lecture: L10 · Outcomes: PF-5.3, PF-5.4 Prerequisites: E-039, E-045 Problem: For all primes p ≤ 500, find consecutive prime pairs (p, q) with q − p = 2. Print each twin pair, then print how many twin pairs were found and the largest gap between consecutive primes in that range. Input: none · Output: pairs + two summary numbers. Sample: (3, 5) (5, 7) (11, 13) … / pairs: … / largest gap: … Hints: generate primes once into an array (or reuse a helper); track previous prime to compute gaps.

PF-E-050 · Harmonic Series with Cutoff

Difficulty: Intermediate · Lecture: L10 · Outcomes: PF-5.2, PF-3.2 Prerequisites: E-030, E-012 Problem: Sum H = 1 + 1/2 + 1/3 + … until the first term that is smaller than a read threshold ε (0.001–0.5). Print the number of terms used and the partial sum (6 decimals). Input: one double · Output: terms + sum. Sample: 0.1 → terms: 11 / H: 3.019877 Hints: loop with double term = 1.0 / i; — floating comparison < (not ==).

PF-E-051 · Palindromic Number Iterator

Difficulty: Intermediate · Lecture: L10 · Outcomes: PF-5.3 Prerequisites: E-033 Problem: Read bounds lo ≤ hi (1–100,000). Print all palindromic numbers in the range (one line, space-separated), then their count. Input: two integers · Output: list + count. Sample: 120 131 → 121 131 / count: 2 Hints: reuse E-033's reversal as the palindrome test — numbers only, no strings.

PF-E-052 · Collatz Longest Chain Under N

Difficulty: Advanced Introductory · Lecture: L10 · Outcomes: PF-5.3, PF-5.4 Prerequisites: E-041 Problem: Read N (2–10,000). Find the starting value ≤ N whose Collatz chain is longest; print that start, its chain length, and the chain's peak. Ties: smallest start wins. Input: one integer · Output: start, length, peak. Sample: 10 → start: 9 / length: 19 / peak: 52 Hints: reuse E-041's chain logic per candidate; track best (length, start) pairs carefully.

PF-E-053 · Goldbach Verification Sweep

Difficulty: Advanced Introductory · Lecture: L10 · Outcomes: PF-5.3, PF-5.4 Prerequisites: E-049 Problem: For every even number 4 ≤ 2k ≤ 200, find one pair of primes (p, q), p ≤ q, with p + q = 2k. Print each even number with its pair, and print verified when all cases succeed. Input: none · Output: 99 lines + verified. Sample: 4 = 2 + 2 / 6 = 3 + 3 / 10 = 3 + 7 Hints: primality helper + a nested search loop with early exit once a pair is found.