# Monthly Archives: August 2019

## If the Sum of the Digits of a Number is Divisible by Three, the Number Is Divisible by Three

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 »

## Can You Find Three Digits for A, B and C Such That ABC in Base-10 Is Equal to CBA in Base-9?

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 »

## Trivia for August 2019

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 »