While in Southern France, Simon really enjoyed solving this puzzle (he originally saw in a Brilliant.org vid). He was so happy with his solution he kept drawing it out on paper and in digital apps, and later shared the puzzle on Twitter. This sparked quite a few reactions from fellow math lovers, encouraged Brilliant to tweet new puzzles and now Brilliant follows Simon on Twitter, how cool is that!
Simon writes: Made a little game where the computer thinks of a number 1-100, and you try to guess it within 7 takes! Hint: the algorithm is called “Binary Search”. https://repl.it/@simontiger/NumberGuessingGame
You can also play the fullscreen version here: https://numberguessinggame.simontiger.repl.run/
Now also a reversed version, where you think of a number and the computer guesses it: https://repl.it/@simontiger/BinaryNumGuessingGame
Simon loves challenging other people with math problems. Most often it’s his younger sister Neva who gets served a new portion of colourful riddles, but guests visiting our home also get their share, as do Simon’s Russian grandparents via FaceTime. Simon picks many of his teaching materials in the Mathematical Fundamentals course on Brilliant.org, and now Neva actually associates “fundamentals” with “fun”!
“What is the chance that two people in a group of, say, 30 people would have their birthday on the same day?” I asked Simon as we were sitting on a bench by the river Schelde late last night, waiting for his Dad and sister to arrive by boat. The reason for this question was that one of the professors at Simon’s MathsJam club turned out to have celebrated his birthday exactly on the same day as I the week before. Besides I was afraid of Simon getting bored just sitting there, “enjoying the warm evening”. At first, I thought he didn’t hear my question and repeated myself a couple of times. Then I noticed he was so silent simply because he was completely immersed in the birthday problem.
Eventually, at that time already on Antwerp’s central square, Simon screamed with joy as he told me the formula he came up with involved triangle numbers! “It’s one minus 364/365 to the power of the 29th triangle number!” he shouted. “It’s a binomial coefficient, the choose function!”
This is a project that Simon started a few weeks ago but never finished, so I think it’s time I archive it here. It’s based upon this wonderful Numberphile video, in which Ben Sparks shows a curious math problem – a game of cat and mouse – in a computer simulation he’d built. The setting is that the mouse is swimming in a round pond and is trying to escape from a cat that is running around the pond. What is the strategy that the mouse should apply to escape, considering that it swims at a quarter of the speed the cat runs?
Simon came up with his own code to recreate the simulation from the Numberphile video. In the four fragments I recorded, he showcases what he has built. Please ignore my silly questions, at the time of the recording I hadn’t viewed the Numberphile video yet and had no idea what the problem entailed.
Sunday at the beach, Simon was reenacting the 5 doors and a cat puzzle (he had learned this puzzle from the Mind Your Decisions channel). The puzzle is about guessing behind which door the cat is hiding in as few guesses as possible, while the cat is allowed to move one door further after every wrong guess.
“Here’s a fun fact!” Simon said all of a sudden. “If you add up all the grains of sand on all the beaches all over the world, you are going to get several quintillion sand grains or several times 10^18!” He then proceeded to try to calculate how many sand grains there might be at the beach around us…
In the evening, while having a meal by the sea, Simon challenged Dad with a Brilliant.org problem he particularly liked:
Simon’s explanation sheet (The general formulas are written by Simon, the numbers underneath the table are his Dad’s, who just couldn’t believe Simon’s counterintuitive solution at first and wanted check the concrete sums. He later accepted his defeat):
Simon finds the explanation on Brilliant.org incomplete, so he started a discussion about it on the Brilliant community page: https://brilliant.org/discussions/thread/games-of-chance-course-marble-problem/?ref_id=1570424