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use the digits from 0 to 9 twice to fill in the 20 spaces in this multiplication problem.

_ _ _
x _ _ _
__________
_ _ _
_ _ _
_ _ _
__________
_ _ _ _ _

2007-10-30 11:36:41 · 2 answers · asked by Anonymous in Science & Mathematics Mathematics

2 answers

179
x224
-----------
716
358
358
-----------
40096

2007-10-31 02:56:37 · answer #1 · answered by Wa Lao 6 · 1 0

0, 1 and 5 not in the end.
0 must be in the middle.

100a + 10b + c => L1
100x + 10y + z => L2
-----------------------------------
[....][....][az][bz][cz] => L3
[....][ay][by][cy] => L4
[ax][bx][cx] => L5
------------------------------------
[p][q][r][s][t] => L6

1 < ax, ay, az < 10
a and x cant both be 1.
0 mist be in the middle (obviously) and cannot be in L2.
so x = y = z =/ 0
0 < x, y, z < 5
0 < a < 4
a = (0, 4)
c, z =/ 0, 1, 5

if x = 1, then L1 = L5
if y = 1, then L1 = L4

also if either one of x, y = 1,
then the other and any of L1 (a,b,c) will not equal 1.
a, b, and c must all be distinct.

from here UD(m) means unit digit of m

UD(cz) cannot equal either one of c or z, but it will equal t.
p will at least be 1 more than a.
since 0 < x, y, z < 5 and 0 < a < 4, b must be big enough so that (ay + bx) >= 10, meaning b cannot be 0 as well.
so L1 AND L2 do not contain any 0.

maybe if there's any repetition in L2, then there must also be a repetition in the answer (L6).

i give up.

2007-10-31 05:46:00 · answer #2 · answered by Mugen is Strong 7 · 1 0

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