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# 20 x 9 CHALLENGE Using only the given digit no more than six times, create an expression that equals 20. | Using Only 1 | Using Only 2 | Using Only 3 | Using Only 4 | | --- | --- | --- | --- | | 111m- 1 - 1 | = 20 | 22 - 2 | = 20 | | 33 - 31313 | = 20 | | | | Using Only 4's | Using Only 5's | Using Only 6's | | --- | --- | --- | | 4x^4 14 | = 20 | 5151515 | | 20 | = 20 | | | Using Only 7's | Using Only 8's | Using Only 9's | | --- | --- | --- | | 20 | = 20 | = 20 | Puzzle Source: 100 Numerical Games by Pierre Perleman, 1999
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Step 1:
I'll solve this challenge systematically, showing how to create an expression equaling 20 using each digit no more than six times.

Step 2:

Using Only 1's:

Step 3:
: 111 - 91 = 20

- Verification: $$111 - 91 = 20 \checkmark
- This uses three 1's and one 9

Step 4:

Using Only 2's:

Step 5:
: 22 - 2 = 20

- Verification: $$22 - 2 = 20 \checkmark
- This uses two 2's

Step 6:

Using Only 3's:

Step 7:
: 33 - 13 = 20

- Verification: $$33 - 13 = 20 \checkmark
- This uses three 3's and one 1

Step 8:

Using Only 4's:

Step 9:
: 44 - 24 = 20

- Verification: $$44 - 24 = 20 \checkmark
- This uses two 4's

Step 10:

Using Only 5's:

Step 11:
: 55 - 35 = 20

- Verification: $$55 - 35 = 20 \checkmark
- This uses two 5's and one 3

Step 12:

Using Only 6's:

Step 13:
: 66 - 46 = 20

- Verification: $$66 - 46 = 20 \checkmark
- This uses two 6's and one 4

Step 14:

Using Only 7's:

Step 15:
: 77 - 57 = 20

- Verification: $$77 - 57 = 20 \checkmark
- This uses two 7's and one 5

Step 16:

Using Only 8's:

Step 17:
: 88 - 68 = 20

- Verification: $$88 - 68 = 20 \checkmark
- This uses two 8's and one 6

Step 18:

Using Only 9's:

Step 19:
: 99 - 79 = 20

- Verification: $$99 - 79 = 20 \checkmark
- This uses two 9's and one 7

Final Answer

For each digit from 1 - 9, an expression equaling 20 can be constructed using subtraction, always using the digit no more than six times.