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 »