Solutions: Sec 3.12 Games

Page 72: Games

Game #2: Reach 99. Add 1-10. Strategy: Target: 99. Step size: $10+1 = 11$. Winning numbers: $99, 88, 77, 66, 55, 44, 33, 22, 11$. First move: Say 11. Then whatever opponent adds ($x$), you add ($11-x$).

Figure It Out (Page 72) Q3. 5-digit odd digits only (1, 3, 5, 7, 9). Range: 35,000 to 75,000. Digits must be odd.

• Largest: Start with 7 (can’t be 9, >75k). Next digits max possible: 9.
  • 73,999 (Wait, range is up to 75,000. 75,111 is > 75,000. 73,999 is valid).
  • Correction from solutions: Solution says 73,999.
• Smallest: Start with 3. Next digits min possible: 5 (wait, range starts at 35,000).
  • Min: 35,111.
• Closest to 50,000:
  • Below: 39,999 (dist 10,001) - Wait, digits must be odd. 39,999 is valid.
  • Above: 51,111 (dist 1,111).
  • Answer: 51,111.

Q6. One 5-digit + Two 3-digit = 18,670. Example: $18,000 + 335 + 335 = 18,670$. Textbook Example: $18,000 + 300 + 370$.