After running afoul of the law in a foreign country, Wyoming Smith (not the guy with a similar name from the Harrison Ford movies) is presented with a logic problem: solve the riddle, or be force-fed crackers until he perishes. (“Snacks? Why does it always have to be snacks??!?” he cried.) The local magistrate offered the following problem:
Before you is a pan balance. Using at most ten (10) different scale weights, how many different consecutive values of weights can you measure exactly? Use only whole number units of grams, and any gaps in numbers available will end your count.
Wyoming solved the problem quickly, and was almost on his way when he spied the magistrate’s magnificent hat. “Double or nothing for the chapeau,” said Wyoming.
The magistrate quickly agreed, and re-issued the same challenge, but allowed Wyoming to place weights on both sides of the pan balance.
Wyoming once again solved the problem quickly, and was on his way with his new lid.
For your chance at this week’s $50 ThinkGeek gift certificate, there are two questions:
- How did Wyoming Smith save his life? That is, what weight sizes (in whole number units of grams) did he select, and with them, how many different consecutive measures could he create using only one side of the pan balance?
- How did Wyoming Smith gain the magistrate’s hat? What weight sizes (in whole number units of grams) did he select, and with them, how many different consecutive measures could he create using both sides of the pan balance?
Note that in both cases, Wyoming could use at most ten (10) difference scale weights. Please forward your answer (and an option picture of you in your favorite hat) to GeekDad Central. All correct entries will be put into a single container and the randomly chosen winning entry will win this week’s $50 ThinkGeek gift certificate. Perhaps we could draw the winning entry from a pot… or maybe a bucket? In any case, good luck, and I look forward to some interesting pictures of our puzzle participants!