Multiples of FourDate: 10/22/2001 at 18:02:17 From: Jenny Subject: Multiples of four How many multiples of four from 1 through 1000 do not contain any of the digits 6, 7, 8, 9, or 0? I don't understand this at all. Date: 10/23/2001 at 12:55:14 From: Doctor Sarah Subject: Re: Multiples of four Hi Jenny - thanks for writing to Dr. Math. We could start by listing multiples of 4 and looking for patterns. Do you know what a multiple of a number is? It's that number multiplied by another number. So the first multiple of 4 is 4x1, the second multiple of 4 is 4x2=8, the third multiple of 4 is 4x3=12, etc. Let's make a table of multiples of 4 from 1 to 100, with columns A-E across the top and rows 1-5 down the left-hand side: A B C D E 1 4 8 12 16 20 2 24 28 32 36 40 3 44 48 52 56 60 4 64 68 72 76 80 5 84 88 92 96 100 Now let's look at these multiples, remembering that there will be nine more tables like this one from 101-1000. Let's look for 6,7,8,9, and 0 in the columns first. Aha! We can erase all of columns B, D, and E because there's a 6 or an 8 or a 0 in each number in those columns. Now we're left with just: A C 1 4 12 2 24 32 3 44 52 4 64 72 5 84 92 Now let's look at the rows. Wow! We can eliminate rows 4 and 5 because they have 6, 7, 8, or 9, leaving: A C 1 4 12 2 24 32 3 44 52 Just 6 numbers left! So if from 1-100 there are 6 multiples of four that do not contain any of the digits 6, 7, 8, 9, or 0, how many multiples of four like this are there from 1-1000? - Doctor Sarah, The Math Forum http://mathforum.org/dr.math/ |
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