1

Part of 2016 May Olympiad

Problems(2)

max interchangeable 4-digit May Olympiad (Olimpiada de Mayo) 2016 L2 P1

Source:

We say that a four-digit number

\overline{abcd}

, which starts at

a

d

, is interchangeable if there is an integer

n >1

n \times \overline{abcd}

is a four-digit number that begins with

d

a

1009

is interchangeable since

1009\times 9=9081

. Find the largest interchangeable number.

number theoryDigits

7 numbers with product perfect cube 2016 May Olympiad L1 p1

Source:

Seven different positive integers are written on a sheet of paper. The result of the multiplication of the seven numbers is the cube of a whole number. If the largest of the numbers written on the sheet is

N

, determine the smallest possible value of

N

. Show an example for that value of

N

and explain why

N

cannot be smaller.

number theoryperfect cubes