Xmas Puzzle 2020 (1)

Instead of using a PLC to test for solutions to the right-hand equation, I think I'll have an attempt at writing a program for an Arduino Nano, possibly using Heap's algorithm rather than attempt to reject value sets that don't meet the criteria.

Actually might be able to do this on an ESP8266 WiFi module, as I don't need either of the 2 GPIO pins, get the results sent to my phone, perhaps.

Again, I'll be looking for non-contentious solutions only..

Might get chance to look at this tomorrow.
 
I like brute force but generating all the permutations is not required.


Yes, it is easily provable that a<4 for the left-hand formula*, and with a bit more work I think that is also true for the right-hand formula*.


Also a>1, maybe so a=2 and a=3 only.



* if a<b and a<c, and conventional solutions.
 
Here are the solutions I've found so far.

First, the four non-contentious ones

2/4 = 3/6 = 79/158

3/6 = 7/14 = 29/58

3/6 = 9/18 = 27/54

2/6 = 3/9 = 58/174

Next, eight that I don't consider contentious, but include the digit, zero.

2/4 = 3/6 = 85/170

2/4 = 5/10 = 38/76

2/4 = 5/10 = 39/78

2/4 = 8/16 = 35/70

2/4 = 9/18 = 35/70

4/8 = 5/10 = 36/72

4/8 = 6/12 = 35/70



Next, four more with zero, but somewhat contentious.

1/4 = 7/28 = 09/36

1/7 = 4/28 = 09/63

1/9 = 3/27 = 06/54

2/3 = 6/9 = 54/081

2/6 = 3/9 = 18/054

Finally, eight contentious solutions with a decimal point.

2/1 = 6/3 = 97/48.5

2/1 = 7/3.5 = 96/48

2/1 = 9/4.5 = 76/38

.4/2 = 1/5 = 76/380

.4/2 = 1/5 = 78/390

.5/4 = 1/8 = 37/296

.5/4 = 1/8 = 79/632

.5/4 = 1/8 = 92/736
 

Similar Topics

Two brothers were walking down the road. The first brother poses a question to the other: 'If I take the digits 1 through 9 and write them down...
Replies
4
Views
1,747
A mother and child walk down an escalator which is running at constant speed in the downward direction. Once on the escalator, the child walks...
Replies
5
Views
1,993
Find 3 palindromic numbers that, when added together, make 85709 (Numbers are in Base 10) Answers by pm please.
Replies
19
Views
6,436
It was too early for Easter, suppose I could have done Chinese New year, but that's too close to Valentines Day. Two parts : 1. A Logix5000...
Replies
1
Views
1,308
Another puzzle for you - answers by pm again. You have 30 coins which you want to deposit in a bank 10km away. A taxi takes you but can only...
Replies
9
Views
7,550
Back
Top Bottom