Answer the following questions.
1. How would you find out a heavier coin out of 20 coins, 19 of which are of normal weight?
Give a short set of steps.
Answers
Hey ''Bani''!
Thank you for asking this question! ❤
Answer:
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1. Put the coins in two stacks of 10 coins. Place on stack on each arm of the balance scale. One arm will higher. That is the lightest stack of coins.
2. Remove one coin from each stack. If they are now balanced you know you have the different coin separated, but you do not know which one of the two coins it is.
3. To determine determine which coin is the different one
a. Remove all coins but one from the scale.
b. Place one of your two separated coins on the other arm of the balance.
c. If the coins balance then the coin you are looking for is the other separated coin. If the coins do not balance it is the coin you placed on the scale last.
To take this one step farther the minimum number required guarantee that you find the correct coin is - 8 weighings.
1. Start the same way as before.
2. Remove 5 coins from each stack. If they balance remove those coins and place the top three from each of the other two stacks. If they do not balance remove the top three from the stacks still on the scale. [Note: keep track of which groups of six coins balanced]
4. Repeat the weighing-in with stacks of three coins. This time if not balanced remove the top coin. If they do balance get the other three stack from the unbalanced six.
5. Confirm the weigh-in with this stack of 3 coins. It will be unbalanced.
6. Remove the top coin from each stack. If the new stacks of two balance you have now reduced the number of coins you need to test to two. Go to step 8.
7. Remove the top coins from each stack. If unbalanced they odd coin is still on the scale. If balanced the odd coin has just been removed.
8. Remove all coins from the scale. Then go to Step 3 in the previous process using one of the known standard weight coins...
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