# Euler problems/121 to 130

## Problem 121

Investigate the game of chance involving coloured discs.

Solution:

```problem_121 = undefined
```

## Problem 122

Finding the most efficient exponentiation method.

Solution using a depth first search, pretty fast :

```import Data.List
import Data.Array.Diff

depthAddChain 12 branch mins = mins
depthAddChain d branch mins = foldl' step mins \$ nub \$ filter (> head branch)
\$ liftM2 (+) branch branch
where
step da e | e > 200 = da
| otherwise =
case compare (da ! e) d of
GT -> depthAddChain (d+1) (e:branch) \$ da // [(e,d)]
EQ -> depthAddChain (d+1) (e:branch) da
LT -> da

baseBranch = [2,1]

baseMins :: DiffUArray Int Int
baseMins = listArray (1,200) \$ 0:1: repeat maxBound

problem_122 = sum . elems \$ depthAddChain 2 baseBranch baseMins
```

## Problem 123

Determining the remainder when (pn − 1)n + (pn + 1)n is divided by pn2.

Solution:

```problem_123 = undefined
```

## Problem 124

Determining the kth element of the sorted radical function.

Solution:

```problem_124 = undefined
```

## Problem 125

Finding square sums that are palindromic.

Solution:

```problem_125 = undefined
```

## Problem 126

Exploring the number of cubes required to cover every visible face on a cuboid.

Solution:

```problem_126 = undefined
```

## Problem 127

Investigating the number of abc-hits below a given limit.

Solution:

```problem_127 = undefined
```

## Problem 128

Which tiles in the hexagonal arrangement have prime differences with neighbours?

Solution:

```problem_128 = undefined
```

## Problem 129

Investigating minimal repunits that divide by n.

Solution:

```problem_129 = undefined
```

## Problem 130

Finding composite values, n, for which n−1 is divisible by the length of the smallest repunits that divide it.

Solution:

```problem_130 = undefined
```