All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 Cute numbers (Posted on 2018-02-01)
A 10 digit positive integer is called a cute number if its digits are from the set {1,2,3} and every two consecutive digits differ by one.

a. Prove that exactly five digits of a cute number are equal to 2.
b. Find the total number of cute numbers.
c. Prove that the sum of all cute numbers is divisible by 1408.

Source: Romanian math competition

 No Solution Yet Submitted by Ady TZIDON No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 Also | Comment 2 of 4 |
For the third part:
Consider the number N=2222222222
For each cute number M>N whose difference to N is A, it does exists another cute number P<N whose difference to N is -A, and viceversa.

So the sum of all cute numbers is:
N*64=142222222222=1408*101010101.

Edited on February 2, 2018, 6:12 am
 Posted by armando on 2018-02-02 05:30:17

 Search: Search body:
Forums (0)