Use all combining
24 produces a remainder 4 when divided by 5
Find the smallest number which when divided by 7, 9 and 11 produces 1, 2, 3 as remainders
7 – 1 = 5 7 – 2 × 1 = 5
9 – 2 = 7 9 – 2 × 2 = 5
11 – 3 = 8 11 – 2 × 3 = 5
Constant Case: Smallest number when divided by x, y and z leaves remainder a, b, c
x - a = y - b = z - c = common difference d
LCM (a, b, c) – d
Convert to Constant Case: Smallest number when divided by x, y and z leaves remainder a, b, c, where
x - ma = y - mb = z - mc = common difference d
Use all combining
6 professors begin courses of lectures on Monday, Tuesday, Wednesday, Thursday, Friday and Saturday, and announce their intentions of lecturing at intervals of 2, 3, 4, 1, 6, 5 days respectively. The regulations of the University forbid Sunday lectures. When first will all six professors simultaneously find themselves compelled to omit a lecture?
-Mayank