47fc3c6761
* fix: clean-up Project Euler 281-300 * fix: missing image extension * fix: missing power Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> * fix: missing subscript Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
47 lines
1.2 KiB
Markdown
47 lines
1.2 KiB
Markdown
---
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id: 5900f4861000cf542c50ff98
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title: 'Problem 281: Pizza Toppings'
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challengeType: 5
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forumTopicId: 301932
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dashedName: problem-281-pizza-toppings
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---
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# --description--
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You are given a pizza (perfect circle) that has been cut into $m·n$ equal pieces and you want to have exactly one topping on each slice.
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Let $f(m,n)$ denote the number of ways you can have toppings on the pizza with $m$ different toppings ($m ≥ 2$), using each topping on exactly $n$ slices ($n ≥ 1$). Reflections are considered distinct, rotations are not.
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Thus, for instance, $f(2,1) = 1$, $f(2,2) = f(3,1) = 2$ and $f(3,2) = 16$. $f(3,2)$ is shown below:
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<img class="img-responsive center-block" alt="animation with 16 ways to have 3 different toppings on 2 slices each" src="https://cdn.freecodecamp.org/curriculum/project-euler/pizza-toppings.gif" style="background-color: white; padding: 10px;">
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Find the sum of all $f(m,n)$ such that $f(m,n) ≤ {10}^{15}$.
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# --hints--
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`pizzaToppings()` should return `1485776387445623`.
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```js
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assert.strictEqual(pizzaToppings(), 1485776387445623);
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```
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# --seed--
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## --seed-contents--
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```js
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function pizzaToppings() {
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return true;
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}
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pizzaToppings();
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```
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# --solutions--
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```js
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// solution required
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```
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