IBM Ponder This #153 · January 2011

Teacher: Let me teach you the order of letters.
Student: That's boring.
Teacher: So we'll do it using a game.
Student: That's better.
Teacher: You see the pile of 45 beans on the table?
Student: Yes.
Teacher: Choose a letter from the phrase "IBM RULES" and take beans while counting from 'A' to the letter you've selected.
Student: OK. I choose 'B', so counting 'A', 'B', I'll take two beans.
Teacher: Right! Now it's my turn, and I choose 'L' Counting 'A', 'B',...,'L', I'll take 12 beans.
Student: Got it. Now it's my turn. I also choose 'L', taking 12 beans.
Teacher: Now it's my turn again. I choose 'R' and counting 'A','B',...,'R', I'll take 18 beans.
Student: Aha! Now it's my turn, but I can't play since there's only one bean left.
Teacher: So I win.
Student: OK. Let's play again, but this time we'll start with 71 beans.
Teacher: Fine. You start.
Student: If I play 'B', I can guarantee winning.
Teacher: Good work! You are learning fast. Let's play with another phrase: "XXXXXX XXXX".
Student: OK. Write the number 204193/178481 + 2**-40 at base 8 (octal) and I'd like you to start if the N-th digit after the octal point is 1, otherwise I'll start. For example, the 19th octal digit is 7, so I'll start if N=19.
Teacher: Wow, that was fast - you solved the game.

Find a possible crossed-out phrase ("XXXXXX XXXX" above) that would make the above dialogue true.

To clarify: "**" above means exponentiation; so 2**-40 is one over 2 to the 40th power.

Solution

Best opened after a real attempt

To be added.