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Cute numbers (Posted on 2018-02-01) Difficulty: 2 of 5
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    
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re: Also Comment 4 of 4 |
(In reply to Also by armando)

Another way of saying it is that 2^7 * 1111111111 = 142222222208

 142222222208 = 2^7 * 11 * 41 * 271 * 9091

  Posted by Charlie on 2018-02-02 13:29:18
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