base-representation-digit-count
Report how many digits a huge number occupies in a given base without ever writing the number out: factor out the largest power of the base that divides it, then bracket the surviving factor between two consecutive powers of that same base. The digit count is the two exponents plus one. The decisive move is refusing to evaluate the number at all — the question asks for its magnitude class, not its value.
풀이 전략
- Keep the 2^a times 5^b shape but make the two exponents unequal so a genuine residual power of 2 or 5 survives the pairing instead of collapsing to a clean power of ten
- Move target_base off 10 to 5 or 7 so the residual must be compared against powers of the new base rather than read off as ordinary digits
- Supply an approximation such as log base ten of 5 is about 0.7 and raise the exponents until hand evaluation is plainly hopeless
세부 유형 분포 (2)
한 줄을 클릭하면 그 안의 문제를 볼 수 있어요.
- power-of-base-extraction 83% (5)
The number arrives as a product of prime powers; pair the prime factors that multiply to the base to pull out a clean power of it, count the digits of whatever factor survives, and add the two counts. Includes the easiest case, where nothing survives and the answer is just the exponent plus one.
- leading-zero-complement 17% (1)
The quantity is a reciprocal or other small fraction and the question asks how many zeros stand between the decimal point and the first significant digit; rewrite it as an integer over a power of ten, count that integer's digits, and subtract from the exponent.
더 보기 (연도 추세, 도구 fingerprint, 학년 분포, 전체 문제)
도구 fingerprint (1–17)
학년 분포
- Gr 6 1
- Gr 8 2