# Difference between revisions of "Euler problems/111 to 120"

m (Corrected links to the Euler project) |
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Line 21: | Line 21: | ||

Solution: |
Solution: |
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<haskell> |
<haskell> |
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− | problem_113 = undefined |
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+ | import Array |
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+ | |||

+ | mkArray b f = listArray b $ map f (range b) |
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+ | |||

+ | digits = 100 |
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+ | |||

+ | inc = mkArray ((1, 0), (digits, 9)) ninc |
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+ | dec = mkArray ((1, 0), (digits, 9)) ndec |
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+ | |||

+ | ninc (1, _) = 1 |
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+ | ninc (l, d) = sum [inc ! (l-1, i) | i <- [d..9]] |
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+ | |||

+ | ndec (1, _) = 1 |
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+ | ndec (l, d) = sum [dec ! (l-1, i) | i <- [0..d]] |
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+ | |||

+ | problem_113 = sum [inc ! i | i <- range ((digits, 0), (digits, 9))] |
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+ | + sum [dec ! i | i <- range ((1, 1), (digits, 9))] |
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+ | - digits*9 -- numbers like 11111 are counted in both inc and dec |
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+ | - 1 -- 0 is included in the increasing numbers |
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</haskell> |
</haskell> |
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+ | Note: inc and dec contain the same data, but it seems clearer to duplicate them. |
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== [http://projecteuler.net/index.php?section=view&id=114 Problem 114] == |
== [http://projecteuler.net/index.php?section=view&id=114 Problem 114] == |

## Revision as of 22:22, 15 August 2007

## Contents

## Problem 111

Search for 10-digit primes containing the maximum number of repeated digits.

Solution:

```
problem_111 = undefined
```

## Problem 112

Investigating the density of "bouncy" numbers.

Solution:

```
problem_112 = undefined
```

## Problem 113

How many numbers below a googol (10100) are not "bouncy"?

Solution:

```
import Array
mkArray b f = listArray b $ map f (range b)
digits = 100
inc = mkArray ((1, 0), (digits, 9)) ninc
dec = mkArray ((1, 0), (digits, 9)) ndec
ninc (1, _) = 1
ninc (l, d) = sum [inc ! (l-1, i) | i <- [d..9]]
ndec (1, _) = 1
ndec (l, d) = sum [dec ! (l-1, i) | i <- [0..d]]
problem_113 = sum [inc ! i | i <- range ((digits, 0), (digits, 9))]
+ sum [dec ! i | i <- range ((1, 1), (digits, 9))]
- digits*9 -- numbers like 11111 are counted in both inc and dec
- 1 -- 0 is included in the increasing numbers
```

Note: inc and dec contain the same data, but it seems clearer to duplicate them.

## Problem 114

Investigating the number of ways to fill a row with separated blocks that are at least three units long.

Solution:

```
problem_114 = undefined
```

## Problem 115

Finding a generalisation for the number of ways to fill a row with separated blocks.

Solution:

```
problem_115 = undefined
```

## Problem 116

Investigating the number of ways of replacing square tiles with one of three coloured tiles.

Solution:

```
problem_116 = undefined
```

## Problem 117

Investigating the number of ways of tiling a row using different-sized tiles.

Solution:

```
problem_117 = undefined
```

## Problem 118

Exploring the number of ways in which sets containing prime elements can be made.

Solution:

```
problem_118 = undefined
```

## Problem 119

Investigating the numbers which are equal to sum of their digits raised to some power.

Solution:

```
problem_119 = undefined
```

## Problem 120

Finding the maximum remainder when (a − 1)n + (a + 1)n is divided by a2.

Solution:

```
problem_120 = undefined
```