[Rearrange this equation Using only move of one stick.L+VIII=X]

Spoiler

Take the horizontal stick of L to the right of equal sign, revised equation becomes 1+8=9

 

[Puzzle with banknotes]

7 hours ago, harey said:

And what about this:

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1: 100                                 pay 10 with 100
2:  50 20 20                           pay  9 with  20
3:  50 20 10  1                        pay  8 with  10
4:  50 20  1  1  1                     pay  9 with  20
5:  50 10  1  1  1  1                  pay  8 with  10
6:  50  1  1  1  1  1  1               pay 10 with  50
7:  20 20  1  1  1  1  1  1            pay  9 with  20
8:  20 10  1  1  1  1  1  1  1         pay  8 with  10
9:  20  1  1  1  1  1  1  1  1  1      pay 18 with  20
     1  1  1  1  1  1  1  1  1  1  1

 

I think I can improve your solution to 10 toys instead of 9, You are welcome to improve better!

But your solution as well as mine both are subject to a big IF - the acceptance of  my note below.

 

1:  100                                                                                cash 100              pay 5 with 100      get 50 20 20 5

2:  50 20 20 5                                                                    cash 95                pay 3 with  5          get 1 1

3:  50 20 20 1 1                                                                 cash 92                pay 5 with 20         get 10 5

4:  50 20 10 5  1 1                                                             cash 87                pay 3 with 5           get 1 1

5:  50 20 10 1 1 1 1                                                           cash 84                pay 8 with 10         get 1 1

6:  50 20 1 1 1 1 1 1                                                          cash 76                pay 9 with 20         get 10 1

7:  50 10 1 1 1 1 1 1 1                                                       cash 67                pay 8 with 10         get  1 1

8:  50  1 1 1 1 1 1 1 1 1                                                     cash 59                pay 10 with 50       get  20 20

9:  20 20 1 1 1 1 1 1 1 1 1                                                 cash 49                pay 18 with 20       get 1 1

10: 20 1 1 1 1 1 1 1 1 1 1 1                                               cash 31                pay 18 with 20        get 1 1

Balance all small change .........                                       cash 13                END

With the best utilization of 87%!! 

 

Notes:

Problem-setter's solution (of 8 toys) seems to interpret the rule 4 as "...............return the change with as less banknotes as possible,............ at the end it turns out that each seller always return at least two banknotes to George". (BOTH OF THESE HIGHLIGHTED CONDITIONS MUST BE COMPLIED IN TOGETHER AND HENCE COMPLIED ACCORDINGLY).

Whereas in your as well as mine (of 9 toys & 10 toys respectively), the interpretation of rule 4 is as " .......... always return  at least two bank notes. Therefore, if at any stage return of 1 banknote alone becomes possible, ignore such option and simply stick to return 2 banknotes instead....." 

I have interpreted so (with more liberty than the problem-setter), especially because the word "always" has NOT been used by the problem-setter in the first part of the highlighted conditions . Word "always" has been used by him in second part of the highlighted condition only.

[Puzzle with banknotes]

I think I have a much better answer.

01: 100                                                                                                                                                    pay 3 with 100

02: 50 20 20 10 5 2                                                                                                                                pay 3 with 5

03: 50 20 20 10 2 1 1                                                                                                                  

On 5/17/2020 at 9:42 PM, harey said:

I think I can do better:

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01:   100                                   pay 10 with 100
02:   50 20 20                              pay  5 with  50
03:   20 20 20 20  5                        pay  3 with   5
04:   20 20 20 20  1  1                     pay  5 with  20
05:   20 20 20 10  5  1  1                  pay  3 with   5
06:   20 20 20 10  1  1  1  1               pay  8 with  10
07:   20 20 20  1  1  1  1  1  1            pay  9 with  20
08:   20 20 10  1  1  1  1  1  1  1         pay  8 with  10
09:   20 20  1  1  1  1  1  1  1  1  1      pay 18 with  20
10:   20  1  1  1  1  1  1  1  1  1  1  1   pay 18 with  20

But not sure it is the max.

@harey  Rule 3 in the puzzle stipulated

 "..........always gives  the nearest bank note (of which he had at the moment)....". 

You have broken this rule at shop 02, by tendering a note of denomination 50. You MUST have tendered note of denomination 20 intead!!