I found this in that most prestigious of publications American Way magazine (free on American Airlines). It was in a “Mensa Quiz” on page 68…
Replace the letters wtih the proper numbers to make this puzzle work (the dots are just for spacing purposes):
…HE
x…ME
…BE
+.YE
EWE
the solution is given as this:
…15
x…35
…75
+.45
…525
Which looks nice and all, assuming that you live in Bizarro World where 15 x 35 = 75…
I despise math (hey, I’m allowed–I’m a girl) and so I ain’t gonna figure it out on my own…but what is the real solution.
What you have here is the old method of multiplication when you’re multiplying two numbers that are at least two digits long. You break up one of the numbers into its individual digits and add the results. Like this:
15 × 35
= 15 × (3 × 10 + 5)
= (15 × 3) × 10 + (15 × 5)
= 45 × 10 + 75
= 525
This is easier to do, because we can multiply by one digit at a time. The means of writing it out with the columns aligned like they are is traditional way of writing multiplication problems by hand, for people who can’t do math in their heads and don’t have access to calculators. Does that make sense?
The same thing Achernar says. I will use zeros as spacers.
015
x35
First you take the 15 and multiply it times the second digit in the 35, the 5.
015
xx5
075
Then you multiply 15 times the first digit of 35, or the 3, remembering to put an x as a place holder.
015
x30
45x
0075
+45
0525
You youngsters with your fancy gadget calculator thingies never learned to show your work. That’s how you end up writin’ for newfangled magazines like American what-not.
Aha. I do know that but hadn’t been looking at the equation that way. I was looking at it as
(HE x ME) + YE = EWE
I wasn’t looking at it as a show-your-work thing.
It makes sense now.
The trick is the plus sign. I have never seen any child taught to actually write the plus sign alongside the product of the “tens” multiplication, so seeing a plus sign in the first equation makes it appear as if the BE should be the complete answer to the multiplication and that YE is a new term to be added to the product in order to produce the sum EWE.
The clue that they were inserting an extraneous plus sign is that YE is offset to the left–which is where the product of HE x M belongs (with M0 understood and the trailing (understood) zero represented by the space to the right of YE).
Well in the magazine, the + YE was just down on a new line, so it didn’t really seem so much “lined up” as just left-justified.
The other clue would be that you can’t multiply two two digit numbers and get a two digit number. (Now that I’ve seen the answer). But the plus sign is misleading.
Yeah we initially thought that there might have been a typo, and that the two digit number was supposed to be a three digit one and the magazine screwed it up…