chore(i18n,learn): processed translations (#45287)
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---
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id: 5900f4531000cf542c50ff65
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title: 'Problem 230: Fibonacci Words'
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title: 'Problema 230: Parole di Fibonacci'
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challengeType: 5
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forumTopicId: 301874
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dashedName: problem-230-fibonacci-words
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@ -8,32 +8,36 @@ dashedName: problem-230-fibonacci-words
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# --description--
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For any two strings of digits, A and B, we define FA,B to be the sequence (A,B,AB,BAB,ABBAB,...) in which each term is the concatenation of the previous two.
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Per due stringhe di cifre, $A$ e $B$, definiamo $F_{A,B}$ come la sequenza ($A, B, AB, BAB, ABBAB, \ldots$) in cui ogni termine è la concatenazione dei due precedenti.
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Further, we define DA,B(n) to be the nth digit in the first term of FA,B that contains at least n digits.
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Inoltre, definiamo $D_{A,B}(n)$ come la $n$-sima cifra nel primo termine di $F_{A,B}$ che contiene almeno $n$ cifre.
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Example:
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Esempio:
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Let A=1415926535, B=8979323846. We wish to find DA,B(35), say.
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Sia $A = 1\\,415\\,926\\,535$, $B = 8\\,979\\,323\\,846$. Vogliamo trovare, diciamo, $D_{A,B}(35)$.
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The first few terms of FA,B are: 1415926535 8979323846 14159265358979323846 897932384614159265358979323846 14159265358979323846897932384614159265358979323846
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I primi termini di $F_{A,B}$ sono:
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Then DA,B(35) is the 35th digit in the fifth term, which is 9.
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$$\begin{align} & 1\\,415\\,926\\,535 \\\\ & 8\\,979\\,323\\,846 \\\\ & 14\\,159\\,265\\,358\\,979\\,323\\,846 \\\\ & 897\\,932\\,384\\,614\\,159\\,265\\,358\\,979\\,323\\,846 \\\\ & 14\\,159\\,265\\,358\\,979\\,323\\,846\\,897\\,932\\,384\\,614\\,15\color{red}{9}\\,265\\,358\\,979\\,323\\,846 \end{align}$$
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Now we use for A the first 100 digits of π behind the decimal point: 14159265358979323846264338327950288419716939937510 58209749445923078164062862089986280348253421170679
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Allora $D_{A,B}(35)$ è la ${35}$-sima cifra nel qunto termine, che è 9.
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and for B the next hundred digits:
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Ora utilizziamo per $A$ le prime 100 cifre di $π$ dietro il punto decimale:
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82148086513282306647093844609550582231725359408128 48111745028410270193852110555964462294895493038196 .
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$$\begin{align} & 14\\,159\\,265\\,358\\,979\\,323\\,846\\,264\\,338\\,327\\,950\\,288\\,419\\,716\\,939\\,937\\,510 \\\\ & 58\\,209\\,749\\,445\\,923\\,078\\,164\\,062\\,862\\,089\\,986\\,280\\,348\\,253\\,421\\,170\\,679 \end{align}$$
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Find ∑n = 0,1,...,17 10n× DA,B((127+19n)×7n) .
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e per $B$ le prossime cento cifre:
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$$\begin{align} & 82\\,148\\,086\\,513\\,282\\,306\\,647\\,093\\,844\\,609\\,550\\,582\\,231\\,725\\,359\\,408\\,128 \\\\ & 48\\,111\\,745\\,028\\,410\\,270\\,193\\,852\\,110\\,555\\,964\\,462\\,294\\,895\\,493\\,038\\,196 \end{align}$$
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Trova $\sum_{n = 0, 1, \ldots, 17} {10}^n × D_{A,B}((127 + 19n) × 7^n)$.
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# --hints--
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`euler230()` should return 850481152593119200.
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`fibonacciWords()` dovrebbe restituire `850481152593119200`.
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```js
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assert.strictEqual(euler230(), 850481152593119200);
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assert.strictEqual(fibonacciWords(), 850481152593119200);
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```
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# --seed--
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@ -41,12 +45,12 @@ assert.strictEqual(euler230(), 850481152593119200);
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## --seed-contents--
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```js
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function euler230() {
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function fibonacciWords() {
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return true;
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}
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euler230();
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fibonacciWords();
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```
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# --solutions--
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