FIVE DISTINCT DIGITS |
Observe these two multiplication examples:
Do you see something uniquely different about the first case that is not true about the second one? Well, the first one is made up of five different, or distinct, digits, whereas the second one has a
repeated digit, the 4.
12
x 5
6012
x 4
48
That in and of itself may not seem so terribly significant, that is, until you try to find all the possible such cases that exist. And when this is presented to young students, say in the 3rd-5th grade levels, it becomes a reasonably decent challenge.
Initially, it can be made into a game. The rules are very simple: Find as many such cases as you can in, say 5 minutes. Score 1 point for each case found. There are more than 30 such cases possible, so there is plenty to keep the contestants busily hunting for that amount of time.
Symbolically, we are looking for solutions to multiplication statements that exhibit this mathematical structure:
AB
x C
DE
Once this activity has run its course, there is always the greater challenge: go for 6 distinct digits! This means to look for multiplications that have the form of
AB
x C
DEF
Happy hunting!
There are only 22 solutions:
58401 = 63x927 32890 = 46x715 26910 = 78x345 19084 = 52x367 17820 = 36x495 & 17820 = 45x396 16038 = 27x594 & 16038 = 54x297 15678 = 39x402 65821 = 7x9403 65128 = 7x9304 34902 = 6x5817 36508 = 4x9127 28651 = 7x4093 28156 = 4x7039 27504 = 3x9168 24507 = 3x8169 21658 = 7x3094 20754 = 3x6918 20457 = 3x6819 17082 = 3x5694 15628 = 4x3907
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