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Due date
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Project description
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2 December
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This puzzle has two unrelated parts.
Show your work.
- Click on this link to see the first of the two
puzzles.
- The second puzzle consists of 3 parts, each next one slightly more work.
- You are given a balance and 3 identical looking coins.
2 of the 3 coins are pure gold.
The 3rd coin is not pure gold, and is slightly lighter than a proper gold coin.
Show how to use the balance exactly 1 time to determine which of the 3 coins is
the one that is slightly lighter.
No trickeries like putting coins on the scales one at the time, just 1 weighing
allowed.
- You are given a balance and 9 identical looking coins.
8 of the 9 coins are pure gold.
The 9th coin is not pure gold, and is slightly lighter than a proper gold coin.
Show how to use the balance exactly 2 times to determine which of the 9 coins
is the one that is slightly lighter.
No trickeries like putting coins on the scales one at the time, just 2
weighings allowed.
- You are given a balance and 27 identical looking coins.
26 of the 27 coins are pure gold.
The 27th coin is not pure gold, and is slightly lighter than a proper gold
coin.
Show how to use the balance exactly 3 times to determine which of the 27 coins
is the one that is slightly lighter.
No trickeries like putting coins on the scales one at the time, just 3
weighings allowed.
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21 October
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This puzzle has three unrelated parts.
Show your work.
- Find three positive integers whose sum equals their product.
- On a national homework problem for 729600 students, 3.5% scores 1 point.
Of the remaining 96.5% of the students, half get 2 points and half get 0.
How many points in total did the students score?
- We are given 12 identical matches.
We can arrange them as edges of polygons in many ways, like:
- When we line them up as boundaries of a square with sides 3, then the
enclosed area equals 9.
- When we line them up as boundaries of a rectangle of width 5 and
height 1, then the enclosed area equals 5.
- If we arrange them as boundary of the blue area below, then the
enclosed area equals 5.
Find a polygon arrangement such that the enclosed area equals 4.
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25 September
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This puzzle has two unrelated parts.
Show your work.
- Put the digits 1 through 8 in the eight green squares below such that
no consecutive digits occur in boxes that touch by an edge or that touch by a
vertex.
- Jack is twice as old as Jill was, when Jack was as old as Jill is now.
Together Jack and Jill are 28 years old.
How old is Jack?
How old is Jill?
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11 September
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This puzzle has two parts:
- Find the sum 100 + 99 + 98 + 97 + ..... + 4 + 3 + 2 + 1.
Show how you got the answer.
Clever mathematical methods are much recommended.
- Find a closed formula for the sum 1 + 11 + 21 + 31 + ..... + (10n-39)
+(10n-29) + (10n-19) + (10n-9) of the first n numbers with right-most digit 1.
Include your work showing why you formula is correct.
As a hint you may want to look at the 3 proofs on
this class page.
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