Math Is Fun Forum

SPACKlick

Member

Registered: 2013-08-21

Posts: 3

Sides Reversed Is Puzzle

Error in the solution to this one

Instead of writing 12 x 42, Horace wrote 21 x 24
Both give the answer 504 because 1 x 4 is the same as 2 x 2.
Instead of writing 12 x 84, Horace wrote 21 x 48
Both give the answer 1008 because 1 x 8 is the same as 2 x 4.
We also know that
1 x 8 is the same as 4 x 2,
1 x 6 is the same as 3 x 2,
and 1 x 6 is the same as 2 x 3.
So the other three questions were 14 x 82, 13 x 62 and 12 x 63.

There are many more;
the components missed are
1*4=2*2
1*9=3*3
2*6=3*4
2*8=4*4
2*9=3*6
3*8=4*6
4*9=6*6
The other questions could have been

1) excluding mirror images
13*93=31*39
23*64=32*46
23*96=32*69
24*63=42*36
24*84=42*48
26*93=62*39
34*86=43*68
36*84=63*48
46*96=64*69

2) excluding all the same digit ones
12*21=21*12
13*31=31*13
14*41=41*14
15*51=51*15
16*61=61*16
17*71=71*17
18*81=81*18
19*91=91*19
23*32=32*23
24*42=42*24
25*52=52*25
26*62=62*26
27*72=72*27
28*82=82*28
29*92=92*29
34*43=43*34
35*53=53*35
36*63=63*36
37*73=73*37
38*83=83*38
39*93=93*39
45*54=54*45
46*64=64*46
47*74=74*47
48*84=84*48
49*94=94*49
56*65=65*56
57*75=75*57
58*85=85*58
59*95=95*59
67*76=76*67
68*86=86*68
69*96=96*69
78*87=87*78
79*97=97*79
89*98=98*89

3) excluding quadruple digits
11*22=11*22
11*33=11*33
11*44=11*44
11*55=11*55
11*66=11*66
11*77=11*77
11*88=11*88
11*99=11*99
22*33=22*33
22*44=22*44
22*55=22*55
22*66=22*66
22*77=22*77
22*88=22*88
22*99=22*99
33*44=33*44
33*55=33*55
33*66=33*66
33*77=33*77
33*88=33*88
33*99=33*99
44*55=44*55
44*66=44*66
44*77=44*77
44*88=44*88
44*99=44*99
55*66=55*66
55*77=55*77
55*88=55*88
55*99=55*99
66*77=66*77
66*88=66*88
66*99=66*99
77*88=77*88
77*99=77*99
88*99=88*99

Quadruple digits
11*11=11*11
22*22=22*22
33*33=33*33
44*44=44*44
55*55=55*55
66*66=66*66
77*77=77*77
88*88=88*88
99*99=99*99

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Sides Reversed Is Puzzle

Hi

The ones in group 1) are valid solutions. The other three groups are invalid as solutions because the problem says that Horace copied all the problems incorrectly. If one of the problems was 12*21 and he switched the digits, he would've got 21*12 which is the same problem.

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