   SEARCH HOME Math Central Quandaries & Queries  Question from charles, a student: Using the digits 0,1,2,3,4 and 5 only once give the smallest 5-digit even number Hi Charles,

I am going to try a smaller problem.

Using the digits 0,1,2, and only once give the smallest 3-digit number which is divisible by 4.

I want a three digit number xyz to be small. The digit that contributes the most to the number is the hundredths digit x so I want it as small as possible. I could make it zero but then the number 0yz = yz is a two digit number so the smallest I can make x is 1. Hence my number so far is 1yz.

It the next step the digit that contributes the most to the number is the tens digit y. I want it as small as possible and this time I can choose zero. Hence I now have 10z.

Finally I want z to be as small as possible so my first suggestion is to let z be 2. But 102 is not divisible by 4 so maybe I need z = 3. Again 103 is not divisible by 4 so what about z = 4? 104 is divisible by 4 so 104 is the number I want.

Can you solve your problem now?
Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.