QQuestionMathematics
QuestionMathematics
# 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
12 months agoReport content
Answer
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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.
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