试着用必剪剪了一下，初次尝试。
狗狗群OUAT《斑马荔枝》
2021-12-10 20:00:00
猫咪吃多少计算工具
2021-11-10 20:00:00
一直拿计算器计算我家灰灰应该吃多少，觉得太麻烦了。
然后就用公式写了一个。
根据计算结果灰灰应该吃80克左右的猫粮或者1.5罐罐头，好像它完全没有根据公式来吃呢。
ICY收发日历
2021-07-28 12:00:00
在ICardYou 上偶尔收发明信片，心血来潮做了个日历。
Problem 63 Powerful digit counts
2019-11-13 08:30:00
The 5-digit number, 16807=\(7^5\), is also a fifth power. Similarly, the 9-digit number, 134217728=\(8^9\), is a ninth power.
How many n-digit positive integers exist which are also an nth power?
Problem 62 Cubic permutations
2019-07-12 08:30:00
The cube, 41063625 ( \(345^3\) ), can be permuted to produce two other cubes: 56623104 ( \(384^3\) ) and 66430125 ( \(405^3\) ). In fact, 41063625 is the smallest cube which has exactly three permutations of its digits which are also cube.
Find the smallest cube for which exactly five permutations of its digits are cube.
Problem 61 Cyclical figurate numbers
2019-07-01 08:30:00
Triangle, square, pentagonal, hexagonal, heptagonal, and octagonal numbers are all figurate (polygonal) numbers and are generated by the following formulae:
| Triangle | \(P_{3,n}=n(n+1)/2\) | 1, 3, 6, 10, 15, … |
| Square | \(P_{4,n}=n2\) | 1, 4, 9, 16, 25, … |
| Pentagonal | \(P_{5,n}=n(3n−1)/2\) | 1, 5, 12, 22, 35, … |
| Hexagonal | \(P_{6,n}=n(2n−1)\) | 1, 6, 15, 28, 45, … |
| Heptagonal | \(P_{7,n}=n(5n−3)/2\) | 1, 7, 18, 34, 55, … |
| Octagonal | \(P_{8,n}=n(3n−2)\) | 1, 8, 21, 40, 65, … |
The ordered set of three 4-digit numbers: 8128, 2882, 8281, has three interesting properties.
- The set is cyclic, in that the last two digits of each number is the first two digits of the next number (including the last number with the first).
- Each polygonal type: triangle (\(P_{3,127}=8128\)), square (\(P_{4,91}=8281\)), and pentagonal (\(P_{5,44}=2882\)), is represented by a different number in the set.
- This is the only set of 4-digit numbers with this property.
Find the sum of the only ordered set of six cyclic 4-digit numbers for which each polygonal type: triangle, square, pentagonal, hexagonal, heptagonal, and octagonal, is represented by a different number in the set.
Problem 60 Prime pair sets
2019-06-27 08:30:00
The primes 3, 7, 109, and 673, are quite remarkable. By taking any two primes and concatenating them in any order the result will always be prime. For example, taking 7 and 109, both 7109 and 1097 are prime. The sum of these four primes, 792, represents the lowest sum for a set of four primes with this property.
Find the lowest sum for a set of five primes for which any two primes concatenate to produce another prime.