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Oleg and (the ghost of) Erdös play the following game. Oleg chooses a non- negative integer a1 with at most 1000 digits.

In Round i the following happens:
Oleg tells the number ai to Erdös, who then chooses a non negative integer bi, and then Oleg defines ai+1 = |ai-bi| or ai+1 = ai + bi.
Erdös wins if a20 is a power of 10, otherwise Oleg wins.

Who is the winner, Oleg or Erdös?

(No Solution Yet, 1 Comments) Submitted on 2017-05-26 by Ady TZIDON    

Difficulty: 3 of 5 N dice (in Probability) Rating: 3.50
In "5 dice" Andy had five regular dice. Now he has a total of N regular dice. He claims that the odds of rolling exactly M sixes is exactly half as likely as rolling (M-1) sixes. (M < N).

For what values of N is this true?

State the pattern if there is one.

Express M as a function of N.

(No Solution Yet, 3 Comments) Submitted on 2017-05-25 by Larry    

Let N(x) be the number 122....221 where the digit 2 occurs x times.

Twice in the past we have determined the highest power of 11 that divides N(2001) is 11^3.

What is the smallest x for N(x) to be a multiple of 11^3? What about multiples of 11^4 and 11^5?
(No Solution Yet, 4 Comments) Submitted on 2017-05-24 by Brian Smith    

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