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Author Archives: benvitalis
Using 9,9,9,9 to make 1-100
Using 9, 9, 9, 9 and the basic operations make the numbers 1 to 100. You may also use decimal points. Here are the numbers 1 to 20: 1 … Continue reading
Triangle (5, 7, 8)
A triangle with sides of length 5, 7, and 8 Perimeter = 20 Area = 10 √3 ~ 17.3205 one of its angles measures 60 degrees: Applying the Law … Continue reading
Primes p; n(p + n) is a square
Consider the first few prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37 And f(p) = n(p + n), where p is an odd prime and … Continue reading
Using 1,2,3,4,5 only once to make 1 – 100
Game: Using 1, 2, 3, 4, 5 only once and the basic operations (+, -, * , / , !) to make all the numbers from 1 to 100 0 = 5 + 3 – (4*2/1) … Continue reading
Num3ers with repeated digits divisible by a prime they contain
Start with a 2-digit prime number 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 and find numbers that repeat the digits of the chosen prime and divisible … Continue reading
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Concatenation | (x – y + z)^3 = x || y || z
Older post: Concatenation: x||y||z = x^3 + y^3 + z^3 Find integers x, y and z such that (x – y + z)^3 = x || y || z … Continue reading
Using Primes 2,3,5,7 only once to make 1-100
Game: You can use the primes 2, 3, 5, 7 and the basic operations +, -, *, / and ! (factorial) only once to make numbers from 1 to 100. … Continue reading
Non-palindrome multiplied by its reverse is a square
For example, 288 is a non-palindrome and a non-square number. Its reverse is: Rev (288) = 882 and, 288 * 882 = 254016 = 504^2 is a perfect … Continue reading
DigitProduct and Sum of prime factors of numbers
(1) Integers such that the sum of prime factors equal the product of the digits of those integers: The prime factors of 18 are: … Continue reading
3-digit Num3ers w/ consecutive digits
123 + 132 + 213 + 231 + 312 + 321 = 1332 (123 + 132 + 213 + 231 + 312 + 321)/2 = 666 (123 + 132 + 213 + 231 + 312 + 321)/3 = 444 (123 … Continue reading
