-
Notifications
You must be signed in to change notification settings - Fork 0
/
problems.txt
137 lines (97 loc) · 4.06 KB
/
problems.txt
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
== 001
Find the sum of all the multiples of 3 or 5 below 1000.
== 002
By considering the terms in the Fibonacci sequence whose values do not exceed
four million, find the sum of the even-valued terms.
== 003
What is the largest prime factor of the number 600851475143 ?
== 004
Find the largest palindrome made from the product of two 3-digit numbers.
== 005
What is the smallest positive number that is evenly divisible by all of the
numbers from 1 to 20?
== 006
Find the difference between the sum of the squares of the first one hundred
natural numbers and the square of the sum.
== 007
What is the 10001st prime number?
== 008
Find the greatest product of five consecutive digits in the 1000-digit number.
<data/008>
== 009
A Pythagorean triplet is a set of three natural numbers, a < b < c,
for which a^2 + b^2 = c^2.
There exists exactly one Pythagorean triplet for which a + b + c = 1000.
Find the product abc.
== 010
Find the sum of all the primes below two million.
== 011
What is the greatest product of four adjacent numbers in any
direction (up, down, left, right, or diagonally) in the 20x20 grid?
<data/011>
== 012
The sequence of triangle numbers is generated by adding the natural numbers.
So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28.
What is the value of the first triangle number to have over five hundred
divisors?
== 013
Work out the first ten digits of the sum of the following one-hundred 50-digit
numbers.
<data/013>
== 014
The following iterative sequence is defined for the set of positive integers:
n -> n/2 (n is even)
n -> 3n + 1 (n is odd)
Which starting number, under one million, produces the longest chain?
== 015
Starting in the top left corner of a 2×2 grid, and only being able to move to
the right and down, there are exactly 6 routes to the bottom right corner.
How many such routes are there through a 20×20 grid?
== 016
2^15 = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26.
What is the sum of the digits of the number 2^1000?
== 017
If the numbers 1 to 5 are written out in words: one, two, three, four, five,
then there are 3 + 3 + 5 + 4 + 4 = 19 letters used in total.
If all the numbers from 1 to 1000 (one thousand) inclusive were written out in
words, how many letters would be used?
NOTE: Do not count spaces or hyphens. For example, 342 (three hundred and
forty-two) contains 23 letters and 115 (one hundred and fifteen) contains 20
letters. The use of "and" when writing out numbers is in compliance with
British usage.
== 018
By starting at the top of the triangle below and moving to adjacent numbers on
the row below, the maximum total from top to bottom is 23.
3
7 4
2 4 6
8 5 9 3
That is, 3 + 7 + 4 + 9 = 23.
Find the maximum total from top to bottom of the triangle below:
<data/018>
== 019
- 1 Jan 1900 was a Monday.
- Thirty days has September, April, June and November. All the rest have
thirty-one, Saving February alone, Which has twenty-eight, rain or shine.
And on leap years, twenty-nine.
- A leap year occurs on any year evenly divisible by 4, but not on a century
unless it is divisible by 400.
How many Sundays fell on the first of the month during the twentieth century
(1 Jan 1901 to 31 Dec 2000)?
== 020
Find the sum of the digits in the number 100!
== 021
Let d(n) be defined as the sum of proper divisors of n (numbers less than n
which divide evenly into n). If d(a) = b and d(b) = a, where a ≠ b, then a
and b are an amicable pair and each of a and b are called amicable numbers.
Evaluate the sum of all the amicable numbers under 10000.
== 022
Using names.txt (right click and 'Save Link/Target As...'), a 46K text file
containing over five-thousand first names, begin by sorting it into
alphabetical order. Then working out the alphabetical value for each name,
multiply this value by its alphabetical position in the list to obtain a name
score.
For example, when the list is sorted into alphabetical order, COLIN, which is
worth 3 + 15 + 12 + 9 + 14 = 53, is the 938th name in the list. So, COLIN
would obtain a score of 938 × 53 = 49714.
What is the total of all the name scores in the file?