If 1+12+123+1234+12345+123456+1234567+12345678is congruent to n modulo 9, where 0≤n<9, what is the value of n?
Solution — click to reveal
A number is congruent to the sum of its digits (mod9). Thus, 1+12+123+1234+12345+123456+1234567+12345678≡1+3+6+10+15+21+28+36(mod9)≡1+3+6+1+6+3+1+9(mod9)≡30(mod9)≡3(mod9).