1) An evil sorcerer has placed three boxes of treasure and a beautiful princess in a magic castle. The princess will sleep until a prince arrives who can guess the contents of the three boxes. Box 1 is labeled diamonds, box 2 rubies, and box 3 diamonds and rubies. One box contains only diamonds, another rubies and the third both, but the sorcerer has lied in his labels. The prince is granted the power to open one of the three boxes and extract one object from it. How can the prince reason to determine what is in each box, and thereby save the princess?
2) What eight-letter word contains only one vowel?
3) You have a balance scale, but the economic crisis has depleted your ability to buy weights for it. What is the least number of weights that will permit you to weigh any number of grams from one through 40, and what are those weights?
AnswersToMarchQuiz: 1) The cube of the numbers starting with one. 2) 33,550,336. This is the series of perfect numbers, those whose divisors add up to the number itself. The next one after is 8,589,869,056. 3) Starting with a billion, add one to the Latin root of the number and multiply by three to find the number of zeros. Thus "bi" is the root for two; add one, which gives three. Multiply by three, which gives the number of zeros in a billion, namely nine. Find the names by the reverse process.
| 10 squared (ie to the power of two, or followed by two zeros) | hundred |
| 10 to the power of 3 | thousand |
| 10………………………………6 | million |
| 10………………………………9 | billion |
| 10…………………………….12 | trillion |
| 10…………………………….15 | quadrillion |
| 10…………………………….18 | quintillion |
| 10…………………………….21 | sextillion |
| 10…………………………….24 | septillion |
| 10…………………………….27 | octillion |
| 10…………………………….30 | nonillion |
| 10…………………………….33 | decillion |
| 10…………………………….36 | undecillion |
| 10…………………………….39 | duodecillion |
| 10…………………………….42 | tredecillion |
| 10…………………………….45 | quattuordecillion |
| 10…………………………….48 | quindecillion |
| 10…………………………….51 | sexdecillion |
| 10…………………………….54 | septendecillion |
| 10…………………………….57 | octodecillion |
| 10…………………………….60 | novemdecillion |
| 10…………………………….63 | vigintillion |
A googol is ten to the power of a hundred. Skewes’ number (related to primes) is ten to the power of ten to the power of ten to the power of 34. To place this in perspective, our hearts beat only a billion times in 26.5 years, and 5.7 times ten to the power of 35 hydrogen atoms would reach across the universe.
4) One; one one; two ones; one two and one one; one one, one two, two ones; three ones, two twos, one one; one three, one one, two twos, two ones.
