| ID | Description / Title | Solved By |
|---|
51 | Find the smallest prime which, by changing the same part of the number, can form eight different primes. | 11354 |
52 | Find the smallest positive integer, x, such that 2x, 3x, 4x, 5x, and 6x, contain the same digits in some order. | 27003 |
53 | How many values of C(n,r), for 1 ≤ n ≤ 100, exceed one-million? | 24558 |
54 | How many hands did player one win in the game of poker? | 12759 |
55 | How many Lychrel numbers are there below ten-thousand? | 21839 |
56 | Considering natural numbers of the form, ab, finding the maximum digital sum. | 23140 |
57 | Investigate the expansion of the continued fraction for the square root of two. | 15415 |
58 | Investigate the number of primes that lie on the diagonals of the spiral grid. | 15005 |
59 | Using a brute force attack, can you decrypt the cipher using XOR encryption? | 16396 |
60 | Find a set of five primes for which any two primes concatenate to produce another prime. | 9063 |
61 | Find the sum of the only set of six 4-digit figurate numbers with a cyclic property. | 9183 |
62 | Find the smallest cube for which exactly five permutations of its digits are cube. | 11369 |
63 | How many n-digit positive integers exist which are also an nth power? | 16935 |
64 | How many continued fractions for N ≤ 10000 have an odd period? | 8058 |
65 | Find the sum of digits in the numerator of the 100th convergent of the continued fraction for e. | 10970 |
66 | Investigate the Diophantine equation x2 − Dy2 = 1. | 7218 |
67 | Using an efficient algorithm find the maximal sum in the triangle? | 38111 |
68 | What is the maximum 16-digit string for a "magic" 5-gon ring? | 7523 |
69 | Find the value of n ≤ 1,000,000 for which n/φ(n) is a maximum. | 13673 |
70 | Investigate values of n for which φ(n) is a permutation of n. | 8618 |
71 | Listing reduced proper fractions in ascending order of size. | 11507 |
72 | How many elements would be contained in the set of reduced proper fractions for d ≤ 1,000,000? | 8603 |
73 | How many fractions lie between 1/3 and 1/2 in a sorted set of reduced proper fractions? | 10616 |
74 | Determine the number of factorial chains that contain exactly sixty non-repeating terms. | 10297 |
75 | Find the number of different lengths of wire that can form a right angle triangle in only one way. | 6656 |
76 | How many different ways can one hundred be written as a sum of at least two positive integers? | 11613 |
77 | What is the first value which can be written as the sum of primes in over five thousand different ways? | 6874 |
78 | Investigating the number of ways in which coins can be separated into piles. | 5983 |
79 | By analysing a user's login attempts, can you determine the secret numeric passcode? | 20259 |
80 | Calculating the digital sum of the decimal digits of irrational square roots. | 7610 |
81 | Find the minimal path sum from the top left to the bottom right by moving right and down. | 13387 |
82 | Find the minimal path sum from the left column to the right column. | 8076 |
83 | Find the minimal path sum from the top left to the bottom right by moving left, right, up, and down. | 6718 |
84 | In the game, Monopoly, find the three most popular squares when using two 4-sided dice. | 4626 |
85 | Investigating the number of rectangles in a rectangular grid. | 9855 |
86 | Exploring the shortest path from one corner of a cuboid to another. | 4663 |
87 | Investigating numbers that can be expressed as the sum of a prime square, cube, and fourth power? | 7995 |
88 | Exploring minimal product-sum numbers for sets of different sizes. | 3314 |
89 | Develop a method to express Roman numerals in minimal form. | 8074 |
90 | An unexpected way of using two cubes to make a square. | 3988 |
91 | Find the number of right angle triangles in the quadrant. | 5989 |
92 | Investigating a square digits number chain with a surprising property. | 16122 |
93 | Using four distinct digits and the rules of arithmetic, find the longest sequence of target numbers. | 4201 |
94 | Investigating almost equilateral triangles with integral sides and area. | 4440 |
95 | Find the smallest member of the longest amicable chain with no element exceeding one million. | 5222 |
96 | Devise an algorithm for solving Su Doku puzzles. | 6498 |
97 | Find the last ten digits of the non-Mersenne prime: 28433 × 27830457 + 1. | 21906 |
98 | Investigating words, and their anagrams, which can represent square numbers. | 4002 |
99 | Which base/exponent pair in the file has the greatest numerical value? | 12484 |
100 | Finding the number of blue discs for which there is 50% chance of taking two blue. | 5821 |
