Disconcerting Division: Newsletter Challenge (April 2020)

Here is the solution (I think):

Clue#1: the remainder is zero, so decimal in quotient has to be ".2" or ".5" since the dividend is a whole number. If quotient has ".2", last digit in divisor is "5" and vice versa.

Clue#2: "_ _ 6", since nothing multiplied by 5 ends in 6, last digit in divisor has to be "2" and last digit in quotient has to be ".5" The first digit in the quotient has to be "3" (3 x 2 = 6) or "8" (8 x 2 = 16) to get "_ _ 6".

Clue#3: There are four digits in dividend (>1000). If the quotient is "AB.5" and the divisor is "C2" then the product of (10*A + B + .5) and (10*C + 2) has to be greater than 1000. This removes 22 combinations of the 180 possible combinations of A, B, and C (2 * 10 * 9).

As far as I can see (unless there is another clue that I missed), there are 158 solutions that work (180-22). Here is a listing of an array P which is the dividend, a 3d array of dimensions 2 x 9 x 9, where A is [3,8], B is [0:9] and C is [1:9]

P =

ans(:,:,1) =

378 978

390 990

402 1002

414 1014

426 1026

438 1038

450 1050

462 1062

474 1074

486 1086

ans(:,:,2) =

693 1793

715 1815

737 1837

759 1859

781 1881

803 1903

825 1925

847 1947

869 1969

891 1991

ans(:,:,3) =

1008 2608

1040 2640

1072 2672

1104 2704

1136 2736

1168 2768

1200 2800

1232 2832

1264 2864

1296 2896

ans(:,:,4) =

1323 3423

1365 3465

1407 3507

1449 3549

1491 3591

1533 3633

1575 3675

1617 3717

1659 3759

1701 3801

ans(:,:,5) =

1638 4238

1690 4290

1742 4342

1794 4394

1846 4446

1898 4498

1950 4550

2002 4602

2054 4654

2106 4706

ans(:,:,6) =

1953 5053

2015 5115

2077 5177

2139 5239

2201 5301

2263 5363

2325 5425

2387 5487

2449 5549

2511 5611

ans(:,:,7) =

2268 5868

2340 5940

2412 6012

2484 6084

2556 6156

2628 6228

2700 6300

2772 6372

2844 6444

2916 6516

ans(:,:,8) =

2583 6683

2665 6765

2747 6847

2829 6929

2911 7011

2993 7093

3075 7175

3157 7257

3239 7339

3321 7421

ans(:,:,9) =

2898 7498

2990 7590

3082 7682

3174 7774

3266 7866

3358 7958

3450 8050

3542 8142

3634 8234

3726 8326

I think it's an April 1 Joke, there are 158 different answers:

Divisor=42, Dividend=1281, Quotient=30.5

Divisor=52, Dividend=1586, Quotient=30.5

Divisor=62, Dividend=1891, Quotient=30.5

Divisor=72, Dividend=2196, Quotient=30.5

Divisor=82, Dividend=2501, Quotient=30.5

Divisor=92, Dividend=2806, Quotient=30.5

Divisor=22, Dividend=1771, Quotient=80.5

Divisor=32, Dividend=2576, Quotient=80.5

Divisor=42, Dividend=3381, Quotient=80.5

Divisor=52, Dividend=4186, Quotient=80.5

Divisor=62, Dividend=4991, Quotient=80.5

Divisor=72, Dividend=5796, Quotient=80.5

Divisor=82, Dividend=6601, Quotient=80.5

Divisor=92, Dividend=7406, Quotient=80.5

Divisor=32, Dividend=1008, Quotient=31.5

Divisor=42, Dividend=1323, Quotient=31.5

Divisor=52, Dividend=1638, Quotient=31.5

Divisor=62, Dividend=1953, Quotient=31.5

Divisor=72, Dividend=2268, Quotient=31.5

Divisor=82, Dividend=2583, Quotient=31.5

Divisor=92, Dividend=2898, Quotient=31.5

Divisor=22, Dividend=1793, Quotient=81.5

Divisor=32, Dividend=2608, Quotient=81.5

Divisor=42, Dividend=3423, Quotient=81.5

Divisor=52, Dividend=4238, Quotient=81.5

Divisor=62, Dividend=5053, Quotient=81.5

Divisor=72, Dividend=5868, Quotient=81.5

Divisor=82, Dividend=6683, Quotient=81.5

Divisor=92, Dividend=7498, Quotient=81.5

Divisor=32, Dividend=1040, Quotient=32.5

Divisor=42, Dividend=1365, Quotient=32.5

Divisor=52, Dividend=1690, Quotient=32.5

Divisor=62, Dividend=2015, Quotient=32.5

Divisor=72, Dividend=2340, Quotient=32.5

Divisor=82, Dividend=2665, Quotient=32.5

Divisor=92, Dividend=2990, Quotient=32.5

Divisor=22, Dividend=1815, Quotient=82.5

Divisor=32, Dividend=2640, Quotient=82.5

Divisor=42, Dividend=3465, Quotient=82.5

Divisor=52, Dividend=4290, Quotient=82.5

Divisor=62, Dividend=5115, Quotient=82.5

Divisor=72, Dividend=5940, Quotient=82.5

Divisor=82, Dividend=6765, Quotient=82.5

Divisor=92, Dividend=7590, Quotient=82.5

Divisor=32, Dividend=1072, Quotient=33.5

Divisor=42, Dividend=1407, Quotient=33.5

Divisor=52, Dividend=1742, Quotient=33.5

Divisor=62, Dividend=2077, Quotient=33.5

Divisor=72, Dividend=2412, Quotient=33.5

Divisor=82, Dividend=2747, Quotient=33.5

Divisor=92, Dividend=3082, Quotient=33.5

Divisor=12, Dividend=1002, Quotient=83.5

Divisor=22, Dividend=1837, Quotient=83.5

Divisor=32, Dividend=2672, Quotient=83.5

Divisor=42, Dividend=3507, Quotient=83.5

Divisor=52, Dividend=4342, Quotient=83.5

Divisor=62, Dividend=5177, Quotient=83.5

Divisor=72, Dividend=6012, Quotient=83.5

Divisor=82, Dividend=6847, Quotient=83.5

Divisor=92, Dividend=7682, Quotient=83.5

Divisor=32, Dividend=1104, Quotient=34.5

Divisor=42, Dividend=1449, Quotient=34.5

Divisor=52, Dividend=1794, Quotient=34.5

Divisor=62, Dividend=2139, Quotient=34.5

Divisor=72, Dividend=2484, Quotient=34.5

Divisor=82, Dividend=2829, Quotient=34.5

Divisor=92, Dividend=3174, Quotient=34.5

Divisor=12, Dividend=1014, Quotient=84.5

Divisor=22, Dividend=1859, Quotient=84.5

Divisor=32, Dividend=2704, Quotient=84.5

Divisor=42, Dividend=3549, Quotient=84.5

Divisor=52, Dividend=4394, Quotient=84.5

Divisor=62, Dividend=5239, Quotient=84.5

Divisor=72, Dividend=6084, Quotient=84.5

Divisor=82, Dividend=6929, Quotient=84.5

Divisor=92, Dividend=7774, Quotient=84.5

Divisor=32, Dividend=1136, Quotient=35.5

Divisor=42, Dividend=1491, Quotient=35.5

Divisor=52, Dividend=1846, Quotient=35.5

Divisor=62, Dividend=2201, Quotient=35.5

Divisor=72, Dividend=2556, Quotient=35.5

Divisor=82, Dividend=2911, Quotient=35.5

Divisor=92, Dividend=3266, Quotient=35.5

Divisor=12, Dividend=1026, Quotient=85.5

Divisor=22, Dividend=1881, Quotient=85.5

Divisor=32, Dividend=2736, Quotient=85.5

Divisor=42, Dividend=3591, Quotient=85.5

Divisor=52, Dividend=4446, Quotient=85.5

Divisor=62, Dividend=5301, Quotient=85.5

Divisor=72, Dividend=6156, Quotient=85.5

Divisor=82, Dividend=7011, Quotient=85.5

Divisor=92, Dividend=7866, Quotient=85.5

Divisor=32, Dividend=1168, Quotient=36.5

Divisor=42, Dividend=1533, Quotient=36.5

Divisor=52, Dividend=1898, Quotient=36.5

Divisor=62, Dividend=2263, Quotient=36.5

Divisor=72, Dividend=2628, Quotient=36.5

Divisor=82, Dividend=2993, Quotient=36.5

Divisor=92, Dividend=3358, Quotient=36.5

Divisor=12, Dividend=1038, Quotient=86.5

Divisor=22, Dividend=1903, Quotient=86.5

Divisor=32, Dividend=2768, Quotient=86.5

Divisor=42, Dividend=3633, Quotient=86.5

Divisor=52, Dividend=4498, Quotient=86.5

Divisor=62, Dividend=5363, Quotient=86.5

Divisor=72, Dividend=6228, Quotient=86.5

Divisor=82, Dividend=7093, Quotient=86.5

Divisor=92, Dividend=7958, Quotient=86.5

Divisor=32, Dividend=1200, Quotient=37.5

Divisor=42, Dividend=1575, Quotient=37.5

Divisor=52, Dividend=1950, Quotient=37.5

Divisor=62, Dividend=2325, Quotient=37.5

Divisor=72, Dividend=2700, Quotient=37.5

Divisor=82, Dividend=3075, Quotient=37.5

Divisor=92, Dividend=3450, Quotient=37.5

Divisor=12, Dividend=1050, Quotient=87.5

Divisor=22, Dividend=1925, Quotient=87.5

Divisor=32, Dividend=2800, Quotient=87.5

Divisor=42, Dividend=3675, Quotient=87.5

Divisor=52, Dividend=4550, Quotient=87.5

Divisor=62, Dividend=5425, Quotient=87.5

Divisor=72, Dividend=6300, Quotient=87.5

Divisor=82, Dividend=7175, Quotient=87.5

Divisor=92, Dividend=8050, Quotient=87.5

Divisor=32, Dividend=1232, Quotient=38.5

Divisor=42, Dividend=1617, Quotient=38.5

Divisor=52, Dividend=2002, Quotient=38.5

Divisor=62, Dividend=2387, Quotient=38.5

Divisor=72, Dividend=2772, Quotient=38.5

Divisor=82, Dividend=3157, Quotient=38.5

Divisor=92, Dividend=3542, Quotient=38.5

Divisor=12, Dividend=1062, Quotient=88.5

Divisor=22, Dividend=1947, Quotient=88.5

Divisor=32, Dividend=2832, Quotient=88.5

Divisor=42, Dividend=3717, Quotient=88.5

Divisor=52, Dividend=4602, Quotient=88.5

Divisor=62, Dividend=5487, Quotient=88.5

Divisor=72, Dividend=6372, Quotient=88.5

Divisor=82, Dividend=7257, Quotient=88.5

Divisor=92, Dividend=8142, Quotient=88.5

Divisor=32, Dividend=1264, Quotient=39.5

Divisor=42, Dividend=1659, Quotient=39.5

Divisor=52, Dividend=2054, Quotient=39.5

Divisor=62, Dividend=2449, Quotient=39.5

Divisor=72, Dividend=2844, Quotient=39.5

Divisor=82, Dividend=3239, Quotient=39.5

Divisor=92, Dividend=3634, Quotient=39.5

Divisor=12, Dividend=1074, Quotient=89.5

Divisor=22, Dividend=1969, Quotient=89.5

Divisor=32, Dividend=2864, Quotient=89.5

Divisor=42, Dividend=3759, Quotient=89.5

Divisor=52, Dividend=4654, Quotient=89.5

Divisor=62, Dividend=5549, Quotient=89.5

Divisor=72, Dividend=6444, Quotient=89.5

Divisor=82, Dividend=7339, Quotient=89.5

Divisor=92, Dividend=8234, Quotient=89.5

Yeah but the numbers have to fit in the boxes....

Yep. I agree with SE but I am impressed you were willing to go though all of those steps you went through to show us how you got there. I don't think I'd have the gumption to do it, no, I know I don't have the gumption... The fact you came up with 158 different answers is beyond what I would have attempted. I was happy with the quick and dirty approach to an (1) answer...

Shut the door,I'm outta here....blub blub blub ........(TMI) (IOMH!)

https://tenor.com/view/get-out-no-hell-nope-gif-10700690

14)1393(99.5

126

133

126

70

70

Sorry, second line wrong? should be two numbers long, not three?

I like a lot your approach and I think your result is correct, but when you state "F x 1E must give a three digit number and this can only happen If E=4 and A=9" I think you should mean A instead of F. Moreover this statement is not so immediate, because also the combination E=8 and A=7 gives the same three digits result of 126. So I would suggest the following correction in your text:

Ax1E must give a three digit number and given that L=6 and E=even, we can see that only the following two combinations are possible:

1) E=8 and A=7, or

2) E=4 and A=9

In both cases the result is 126 (9x14=126, or 7x18=126), so J=1 e K=2.

However, considering true the first combination E=8 and A=7, the only possible value is B=5 (5x18=90), so Q=0, but this do not satisfy R as a single digit (even if O would be 0, we would have 100-90=10, two digits).

By exclusion, the only correct combination is the second, E=4 and A=9, so B=7 (7x14=98), Q=8 and R=7.

You are right, it should be "A x 1E" (and not "F x 1E") and I should have also considered the A=8 and E=7 case. GA from me.

The answer I found was 1365/14=97.5:

Sorry about the layout. I'm not yet familiar enough with how to show things in this environment.