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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    

Difficulty: 4 of 5 First or second? (in Games) Rating: 3.00
Two players alternatively erase some 9 numbers from the sequence 1,2,...,101 until only two remain. The player that starts wins x−54 dollars from the player that plays second, x being the absolute value of the difference between the remaining two numbers.

Would you rather be the first or the second player?
Explain your decision by providing your strategy.

(No Solution Yet, 5 Comments) Submitted on 2017-05-23 by Ady TZIDON    

Difficulty: 2 of 5 5 dice (in Probability) Rating: 3.00
Andy rolls five regular dice.
What is more likely: rolling no sixes or rolling exactly one six?
(No Solution Yet, 2 Comments) Submitted on 2017-05-22 by Ady TZIDON    

A 2 by X rectangle can obviously have 2*X circles of diameter 1 placed inside it without overlapping. What is the smallest integer X where a 2 by X box can have 2*X+1 non-overlapping circles placed inside it?
(No Solution Yet, 5 Comments) Submitted on 2017-05-21 by Brian Smith    

Difficulty: 3 of 5 Seven Point Placement (in Shapes) Rating: 4.00
Find a placement of a set of seven points in a plane such that if any subset of three points is chosen then at least one pair of points from the subset are unit distance apart.
(No Solution Yet, 1 Comments) Submitted on 2017-05-20 by Brian Smith    

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