The number, 1406357289, is a 0 to 9 pandigital number because it is made up of each of the digits 0 to 9 in some order, but it also has a rather interesting sub-string divisibility property:
d2d3d4=406 is divisible by 2
d3d4d5=063 is divisible by 3
d4d5d6=635 is divisible by 5
d5d6d7=357 is divisible by 7
d6d7d8=572 is divisible by 11
d7d8d9=728 is divisible by 13
d8d9d10=289 is divisible by 17
Find the sum of all 0 to 9 pandigital numbers with this property.
Leonardo of Pisa, also known as Fibonacci, recounts that he was given this problem by John of Palermo as part of a mathematical tournament.
Three men possess a pile of money, their shares being 1/2, 1/3, 1/6. Each man takes some money from the pile until nothing is left. The first man returns 1/2 of what he took, the second 1/3 and third 1/6. When the total so returned is divided equally among the men it is found that each then possesses what he is entitled to. How much money was in the original pile, and how much did each man take from the pile?
Note: This is a Diophantine problem so you may just give the smallest whole number solution.
This particular problem is attributed to Alcuin. The wording does not give sufficient information to answer the question without making legal assumptions. Please share your assumptions with your solution.
A dying man left 960 shillings and a pregnant wife. He directed that if a boy was born, he should receive three-quarters of the whole and the child's mother should receive one-quarter. But if a daughter was born, she would receive seven-twelfths, and her mother five-twelfths. It happened however that twins were born - a boy and a girl. How much should the mother receive, how much the son, and how much the daughter?
How many distinct integer solution of the equation