Getting the multiplier, multiplicand and the product with U’s

1. Jan 28, 2009

K Sengupta

In the following long multiplication puzzle, each of the U’s represents a decimal digit from 0 to 9, whether same or different.

Each digit from 0-9 must appear precisely 2 times in the following multiplication.

None of the numbers can contain any leading zero.

......U U U
......U U U
-----------
......U U U
...U U U
U U U
------------------
U U U U U

Determine the multiplier, multiplicand and the product.

Note: The dots are present merely for the sake of formatting, and none of the dots represent a decimal point.

Last edited: Jan 29, 2009
2. Jan 29, 2009

davee123

I don't follow. Why couldn't the answer be:

111 * 111 = 12321
or
111 * 222 = 24642
or
123 * 321 = 39483
etc.

Clearly if all the U's represent the SAME digit, the puzzle is impossible, unless U=0. And if U's are different digits, there are seemingly a plethora of answers, so long as each digit in the 2nd number times the 1st number is smaller than 1000, and obviously the product is less than 100000. What am I missing?

DaveE

3. Jan 29, 2009

K Sengupta

You’re right, davee123.

I really goofed up the problem statement and forgot to add that:

”Each digit from 0-9 must appear precisely 2 times in the following multiplication.”

I have now incorporated the said amendments in the problem text.

I sincerely apologize for the inconvenience caused due to the foregoing.