The coach provides puzzles involving digits as today’s fare.
Piece of Pi
The coach notes that somewhere in the digits of pi, the entirety of any text is encoded if the following scheme is used: space = 00, A = 01, a = 02, B = 03, b = 04 and so on. If we assume random digits in the expansion of pi, it will contain the expression “National Museum of Mathematics” in consecutive order if enough digits are examined.
About how many digits of pi will have to be examined to get a 50% probability of encountering a string of 60 consecutive decimal digits that encodes the museum’s name according to the coach’s scheme?
Making 17 and 27
Produce math expressions in which you may use only +, -, ×, ÷, exponents, decimal points, and parentheses.
(a) Make 17 using 1, 4, and 5 one time each.
(b) Make 27 using 1, 5, and 9 one time each.
|Spread the word:||Tweet|
Solutions to week 124
Cutting the Triangle
Links to all of the puzzles and solutions are on the Complete Varsity Math page.
Come back next week for answers and more puzzles.