Varsity Math 125


The coach provides puzzles involving digits as today’s fare.


Pi Again

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.


Solutions to week 124

The figures below show the three solutions to Cutting the Triangle, and the solution to Square Repair. Note that Puzzle (a) of Cutting the Triangle has an infinite number of additional solutions.

Cutting the Triangle
Cutting the Triangle

Square Repair
Square Repair

Recent Weeks

Week 124: Cutting the Triangle & Square Repair, solutions to Mining Mishap & Pulley Puzzle

Week 123: Mining Mishap & Pulley Puzzle, solutions to Minimum Racket Wear & Rolling Circles

Week 122: Minimum Racket Wear & Rolling Circles, solutions to Tennis Exhibition & Losing Streak

Week 121: Tennis Exhibition & Losing Streak, solutions to Breakfast, Lunch, or Dinner? & The 2018 Puzzle

Week 120: Breakfast, Lunch, or Dinner? & The 2018 Puzzle, solutions to Solar Cap Versus Polar Cap & How Tall is the Pole

Links to all of the puzzles and solutions are on the Complete Varsity Math page.

Come back next week for answers and more puzzles.