MHB Discover All Possible 8-Digit Multiples of 2013 with $A = \overline{20abcd13}$

  • Thread starter Thread starter Albert1
  • Start date Start date
Albert1
Messages
1,221
Reaction score
0
$A=\overline{20abcd13}$ is an 8-digit number ,

also $A$ is a multiple of 2013,please find all possible value of $A$
 
Mathematics news on Phys.org
we know 20132013 multiple of 2013
as 20abcd13 = 20132013 + 201300 * x
so the soultions are 20132013 + 201300 * x as last 2 digits are 13
x= 0 gives 20132013
x =1 gives 20333313
x=2 gives 20534613
x=3 gives 20735913
x=4 gives 20937213
x >=5 gives value outside range
 
Last edited:
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Is it possible to arrange six pencils such that each one touches the other five? If so, how? This is an adaption of a Martin Gardner puzzle only I changed it from cigarettes to pencils and left out the clues because PF folks don’t need clues. From the book “My Best Mathematical and Logic Puzzles”. Dover, 1994.
Back
Top