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Category Archives: Number Puzzles
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
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
Concatenation| Sum of consecutive integers
Goal: To find integers that are the sum of consecutive integers in the number For example, 19 || 0 = 190 = 19+18+17+16+15+14+13+12+11+10+9+8+7+6+5+4+3+2+1+0 20 || 4 = 204 = 20+19+18+17+16+15+14+13+12+11+10+9+8+7+6+5+4 21 … Continue reading
Concatenation| A+B=C and A||B = C^2
Find integers A, B, C such that A + B = C and A || B = C^2 For example, 88 + … Continue reading
Integers such that √a + √b = √x
a, b, x are positive integers such that √a + √b = √x Find the number of solutions for x ≤ 1000 How about √a … Continue reading
