# Euler problems/141 to 150

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< Euler problems(Difference between revisions)

(Removing category tags. See Talk:Euler_problems) |

## Revision as of 01:49, 14 December 2007

## Contents |

## 1 Problem 141

Investigating progressive numbers, n, which are also square.

Solution:

problem_141 = undefined

## 2 Problem 142

Perfect Square Collection

Solution:

problem_142 = undefined

## 3 Problem 143

Investigating the Torricelli point of a triangle

Solution:

problem_143 = undefined

## 4 Problem 144

Investigating multiple reflections of a laser beam.

Solution:

problem_144 = undefined

## 5 Problem 145

How many reversible numbers are there below one-billion?

Solution:

import List digits n {- 123->[3,2,1] -} |n<10=[n] |otherwise= y:digits x where (x,y)=divMod n 10 -- 123 ->321 dmm=(\x y->x*10+y) palind n=foldl dmm 0 (digits n) isOdd x=(length$takeWhile odd x)==(length x) isOdig x=isOdd m && s<=h where k=x+palind x m=digits k y=floor$logBase 10 $fromInteger x ten=10^y s=mod x 10 h=div x ten a2=[i|i<-[10..99],isOdig i] aa2=[i|i<-[10..99],isOdig i,mod i 10/=0] a3=[i|i<-[100..999],isOdig i] m5=[i|i1<-[0..99],i2<-[0..99], let i3=i1*1000+3*100+i2, let i=10^6* 8+i3*10+5, isOdig i ] fun i |i==2 =2*le aa2 |even i=(fun 2)*d^(m-1) |i==3 =2*le a3 |i==7 =fun 3*le m5 |otherwise=0 where le=length m=div i 2 d=2*le a2 problem_145 = sum[fun a|a<-[1..9]]

## 6 Problem 146

Investigating a Prime Pattern

Solution:

problem_146 = undefined

## 7 Problem 147

Rectangles in cross-hatched grids

Solution:

problem_147 = undefined

## 8 Problem 148

Exploring Pascal's triangle.

Solution:

problem_148 = undefined

## 9 Problem 149

Searching for a maximum-sum subsequence.

Solution:

problem_149 = undefined

## 10 Problem 150

Searching a triangular array for a sub-triangle having minimum-sum.

Solution:

problem_150 = undefined