January 2020

**Logic Puzzles**

“Uncle Bob”

Each month in 2020 I plan to feature a different type of logic puzzle. This month it’s …

**?????? ?????**

Ummmm. I can’t reveal the name of this type without giving too much away. Perhaps you’ll think of a good name for this family after you’ve tried a few.

**1. Coincidence?** We begin with some interesting facts about two world leader best buds. Uncle Bob provides this handy table. The bottom row asks a little arithmetic of you and some explanation as well.

Leader |
Angela Merkel |
Donald Trump |

Birth year |
1954 |
1946 |

Age |
65 |
73 |

Elected |
2005 |
2016 |

Years in office |
14 |
3 |

Sums |
???? |
???? |

**2**. **Oh! To Be Nineteen Again!** Pick any single digit 1 through 9 and enter it into every blank in the formula below. Calculate.

**( ___ + ___ – 0.___ ) / 0.___**

**3. Lucky You!** Pick any positive whole number. Add 5 to it. Multiply the result by 21. Now withdraw an even 100, but remember that you did. Multiply what's left by 3. Now repay the 100. Add the digits of you number. If it yields a single digit, you are done and you are lucky, yes? If the digit sum is not a single digit, add those digits. Keep adding until the digit sum turns out to be a single digit, and you are lucky in any case. Can you explain how you got to be so lucky?

**4. Piano Lesson.** Most people find learning to play the piano difficult. Ignoring other factors there remains an overwhelming number of keys – 88 in a full-size keyboard. We think our newly designed “key grid” may help. Any song that you could play on a grand piano, you can play on the 16 squares below. No! I meant to say play on **just four** of the squares below. Directions: Pick any one of the 16 squares and eliminate the rest of its row and column. Pick any square still eligible and then eliminate its row and column. Proceed in like manner to choose two more squares. Add your four choices to confirm that you have covered all the keys.

solutions

January 2020

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