Take a two-digit base-10 number where the digits are represented by ab. This number is equal to 10a + b and the sum of its digits are a + b. The difference between the number and the sum is 9a, which is divisible by three. So a + b is divisible by three, if and only… Read More »
The only 3-digit answer is \(544_9 = 445_{10}\). However, there are answers in other bases: \(211_3 = 112_4\) \(322_5 = 223_6\) \(433_7 = 334_8\) \(544_9 = 445_{10}\) Are you seeing a pattern here? Does the pattern extended to bases higher than 10? Does \(655_{10} = 556_{11}\)? Does \(766_{11} = 667_{12}\)? Cheating a little bit by… Read More »
A tree planted in memory of George Harrison, the lead guitarist of The Beatles, died after being infested by beetles. If the sum of the digits of a number is divisible by three, the number is divisible by three. Likewise, if the sum of the digits of a number is divisible by nine, the number… Read More »
Sphenopalatine ganglioneuralgia is the medical term for brain freeze (ice cream headaches). Oraibi, Arizona has been continuously inhabited since sometime around 1100 CE. St. Augustine, Florida, which makes the claim it is the oldest continuously inhabited settlement in the United States, was not founded until 1565, more than 450 years later. Damascus, Syria has been… Read More »