Puzzles and Quizzes - Day 5

April 15, 2020

 

Our Day 5 printable sheet can be found by clicking here.

 

Answers to Day 4:

 

Quiz - Pyramids of Giza, Wembley Stadium, London Eye, Angel of the North, Leicester Square, Thorpe Park, Eiffel Tower, Sydney Harbour Bridge, Heathrow Airport, Stonehenge.

 

Easier Problem - Weigh two groups of three. If one is heavier, take that group of three and weigh one against one – if one ball is heavier it’s that one, if neither is heavier it must be the other ball. If both groups weigh the same, take the remaining group of two and weigh one against one.

 

Harder Problem (yes, this is very difficult!) -

 

Test 1: Weigh ball 1, 2, 3, 4 versus 5, 6, 7, 8.

If Test 1 does balance: It is one of the balls from 9, 10, 11, or 12. Test 2: Weigh 1, 2, 3 versus 9, 10, 11. If Test 2 does balance, the odd ball is 12. For the third test, compare it to any of the other balls to check whether it is heavier or lighter. If Test 2 doesn't balance, the odd ball is 9, 10, or 11. It is heavier or lighter depending on how the scale tipped in 2.1. For the third test, compare 9 and 10. If they balance, it is 11. If they don't balance, it is whichever one is lighter or heavier (depending on the results from #2).

If Test 1 doesn't balance: We know that 9, 10, 11, and 12 are normal. Test 2: Compare 2, 3, 5 and 7 versus 4, 6, 9 and 10. If Test 2 balances, it is 1 or 8. Compare 1 versus 2. If they are equal, it is ball 8, and it is lighter or heavier depending on how the scale tips in test #1. If they are inequal, it is #1, and it is lighter or heavier depending on how the scale tips in this test (and in test 1). If Test 2 doesn't balance: This is easier to explain if we just say that 1-4 was heavier than 5-8. It works either way. If 2, 3, 5, 7 was heavier than 4, 6, 9, and 10, then it is either that 2 or 3 is heavy, or 6 is light. Weigh 2 versus 3. If they are equal, 6 is light. If 2 is heavier, then 2 is heavy. If 3 is heavier, then 3 is heavy. If 2, 3, 5, 7 is lighter than 4, 6, 9, and 10, then it is either that 5 or 7 is light, or 4 is heavy. Compare 5 versus 7, and interpret as before. If they are equal, 4 is heavy. If 5 is light, 5 is light. If 7 is light, 7 is light.

 

 

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