Are you smarter than a fifth grader?

[Ira Gladnick]

Fifth grade Math Superbowl question:

Let A,B,C,D,E,F,G,H,I represent unique digits from 1 -> 9.

If ABCD X E = FGHI, then what numbers do the letters represent?

Actually, I'm trying to figure this out for my daughter, so would
appreciate description of the method.

[Ira Gladnick]

Post by Ira Gladnick
Let A,B,C,D,E,F,G,H,I represent unique digits from 1 -> 9.
If ABCD X E = FGHI, then what numbers do the letters represent?
Actually, I'm trying to figure this out for my daughter, so would
appreciate description of the method.

btw, in case it's not obvious, the X above represents multiplication..

[Virgil]

Post by Ira Gladnick
Let A,B,C,D,E,F,G,H,I represent unique digits from 1 -> 9.
If ABCD X E = FGHI, then what numbers do the letters represent?
Actually, I'm trying to figure this out for my daughter, so would
appreciate description of the method.

You do it by a gradual process of elimination and trial and error.

For example, one can quickly eliminate E = 1 and a little less quickly,
E = 9.

If E = 5 then D is even and J = 0 and A = 1. And so on.

[Ira Gladnick]

Post by Virgil

Post by Ira Gladnick
Let A,B,C,D,E,F,G,H,I represent unique digits from 1 -> 9.
If ABCD X E = FGHI, then what numbers do the letters represent?
Actually, I'm trying to figure this out for my daughter, so would
appreciate description of the method.

You do it by a gradual process of elimination and trial and error.
For example, one can quickly eliminate E = 1 and a little less quickly,
E = 9.
If E = 5 then D is even and J = 0 and A = 1. And so on.

It's the "gradual" part that got me.

Was hoping someone might have a flash of insight into how to hone in
quickly on a solution.

This was taken from a compilation of past-year Math Superbowl
questions. It's typical of these questions that they seem either very
difficult or very lengthy at first glance, but on further inspection
there is usually some relatively simple way to unravel them.

[Ira Gladnick]

Post by Ira Gladnick
If ABCD X E = FGHI, then what numbers do the letters represent?

btw, in case it's not obvious, the X above represents multipliction.

as a bit of a starter: since there is no carry from the last column,
and since E can't be 1 (would violate uniqueness), A must be less than
5 and E must be in (2..9).

[Dana]

I started with this equation, but I am stuck...

equ = {
1000 a e + 100 b e + 10 c e + d e == 1000 f + 100 g + 10 h + i,

Mathematica suggests only two solutions (a->i):
{1, 7, 3, 8, 4, 6, 9, 5, 2},
{1, 9, 6, 3, 4, 7, 8, 5, 2}

I don't see the technique to solve it yet though.

[Frederick Williams]

Post by Ira Gladnick
Let A,B,C,D,E,F,G,H,I represent unique digits from 1 -> 9.
If ABCD X E = FGHI, then what numbers do the letters represent?

1738 x 4 = 6952
1963 x 4 = 7852