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id	title	challengeType	forumTopicId	dashedName
5900f3ab1000cf542c50febe	Problem 63: Powerful digit counts	5	302175	problem-63-powerful-digit-counts

--description--

The 5-digit number, 16807 = 7⁵, is also a fifth power. Similarly, the 9-digit number, 134217728 = 8⁹, is a ninth power.

Complete the function so that it returns how many positive integers are of length n and an nth power.

--hints--

powerfulDigitCounts(1) should return a number.

assert(typeof powerfulDigitCounts(1) === 'number');

powerfulDigitCounts(1) should return 9.

assert.strictEqual(powerfulDigitCounts(1), 9);

powerfulDigitCounts(2) should return 6.

assert.strictEqual(powerfulDigitCounts(2), 6);

powerfulDigitCounts(3) should return 5.

assert.strictEqual(powerfulDigitCounts(3), 5);

powerfulDigitCounts(4) should return 4.

assert.strictEqual(powerfulDigitCounts(4), 4);

powerfulDigitCounts(5) should return 3.

assert.strictEqual(powerfulDigitCounts(5), 3);

powerfulDigitCounts(6) should return 3.

assert.strictEqual(powerfulDigitCounts(6), 3);

powerfulDigitCounts(7) should return 2.

assert.strictEqual(powerfulDigitCounts(7), 2);

powerfulDigitCounts(8) should return 2.

assert.strictEqual(powerfulDigitCounts(8), 2);

powerfulDigitCounts(10) should return 2.

assert.strictEqual(powerfulDigitCounts(10), 2);

powerfulDigitCounts(21) should return 1.

assert.strictEqual(powerfulDigitCounts(21), 1);

--seed--

--seed-contents--

function powerfulDigitCounts(n) {

  return true;
}

powerfulDigitCounts(1);

--solutions--

function powerfulDigitCounts(n) {
  function countDigits(num) {
    let counter = 0;
    while (num > 0) {
      num = Math.floor(num / 10);
      counter++;
    }
    return counter;
  }

  let numbersCount = 0;

  let curNum = 1;
  while (curNum < 10) {
    let power = n;
    if (power === countDigits(curNum ** power)) {
      numbersCount++;
    }
    curNum++;
  }

  return numbersCount;
}

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