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177 votes
Accepted

Is this duplo train track under too much tension?

First, we can check that there is no angular misalignment. Since 12 curved pieces are needed to make a full circle, the number of left pieces minus the number of right pieces must be a multiple of 12. ...
2012rcampion's user avatar
  • 18.9k
65 votes
Accepted

2 vs. 1.005^200

ACB's user avatar
  • 7,281
50 votes

4,4,2,6,2,10,4,_ sequence from 4th grade packet

Same answer as PDT, just explained differently:
Will.Octagon.Gibson's user avatar
48 votes

Combine 1,3,3,7 to get 10

As quite standard in this kind of hard number puzzle, we can: Another example of this form being the only solution is: Use 1, 2, 3, 8 to make 28 with the unique (up to commutation) solution being:
justhalf's user avatar
  • 6,043
46 votes
Accepted

A colorful dodecahedron

Partial Answer: Solution: Other Solutions: Fun Stuff:
DqwertyC's user avatar
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42 votes
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A strange operator on my new calculator

I think the operation replacing + is Examples Finally the last result produces an error because In fact
hexomino's user avatar
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39 votes

How to solve 1 2 3 4 5 = 5 4 3 2 1 (insert five pluses to make it equal)? A thorough solution needed

Well, here is how I would (and did) solve it: First step: Without the « five + » constraint Second step: Getting rid of some « + » A solution we found: Extra note: finding all solutions
Jujustum's user avatar
  • 3,770
39 votes

Hexominos from pentominos, heptominos from hexominos

Let us start by considering this hexomino: It is clear that there is only one pentomino that can be extended to this: And since we have to use that pentomino, we can tick off several hexominoes that ...
BlueHairedMeerkat's user avatar
38 votes
Accepted

Reducing π to zero (again)

At the time of writing, I am currently at 196 reputation, so I am just under the limit. I believe that you cannot reduce the first 20 digits of $\pi$ to 0.
SquareFinder's user avatar
38 votes
Accepted

Can you tile a 25 x 25 square with a mixture of 2 x 2 squares and 3 x 3 squares?

I think the answer is Consider the following image: Generalizing this result, the question "For which $n$ can an $n \times n$ square be tiled with $2 \times 2$ and $3 \times 3$ squares?" ...
Bubbler's user avatar
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38 votes

Can you tile a 25 x 25 square with a mixture of 2 x 2 squares and 3 x 3 squares?

Very similar to @Bubbler's solution but perhaps a bit simpler:
Albert.Lang's user avatar
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35 votes
Accepted

'SILVER' -> ‘LESIRU' and 'GOLDEN' -> 'LEGOND', so 'NATURE' -> what?

It looks like there's a typo in the question: If so, here is how I solved it: Then the answer is:
Stevish's user avatar
  • 1,345
35 votes
Accepted

Naughty knights

AxiomaticSystem's user avatar
34 votes

If A cents can be paid with B coins then prove that B dollars can be paid with A coins

The reason it works for this set of coins is that Using this fact, you can look at each coin value individually: Since the statement is true for each coin value, it is also true for any combination ...
Jaap Scherphuis's user avatar
34 votes

2 vs. 1.005^200

This is quite easy if you know or The largest of the two numbers is
Jaap Scherphuis's user avatar
34 votes

How many dogs of Oxford are there?

The smallest possible number of dogs is
Destructible Lemon's user avatar
33 votes

Pythagorean pentagons

6 pieces, no flipping required: History: 7 pieces, no flipping required: 8 pieces, requires two flips 9 pieces, requires one flip very similar: 10 pieces, no flipping required not very elegant, ...
loopy walt's user avatar
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33 votes
Accepted

Make the number 606 50 percent bigger

'50 percent greater' means Hence the answer we are looking for is Since the number 606 is written on a sheet of paper, we can achieve the result by an operation called
ACB's user avatar
  • 7,281
32 votes

Capture a laser beam

Assuming that you can create curved mirrors with infinite precision, then you could catch a ray ... About that footnote: If curved mirrors are more expensive then you could simplify the room: A ...
Kris Van Bael's user avatar
32 votes
Accepted

It's what's within the two

The answer to the puzzle is Which we must use to solve it!
Beastly Gerbil's user avatar
32 votes

Make 27 using 1, 1, 1, 1

$3/(1/9)=$
Oscar Lanzi's user avatar
32 votes

Pythagorean pentagons

My efforts to minimize the number of pieces did not improve upon loopy walt's best, but here is another 7-piece solution without flipping: Sixteen pieces, with some flipping required.
Daniel Mathias's user avatar
31 votes

Let's make a huge number with only tiny numbers

My answer is Another solution, again with no concatentation A solution using base 6, working in the other direction.
Weather Vane's user avatar
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31 votes
Accepted

2048: How many turns did I survive?

tehtmi's user avatar
  • 3,326
31 votes
Accepted

Join six cities with roads

msh210's user avatar
  • 12.9k
28 votes
Accepted

12 piece cube packing puzzle

What a great puzzle! For me the key was to notice that you will quickly run out of corners. Since there is only one other way (plus a zillion symmetries) to place the hexacube, this means that we ...
Bass's user avatar
  • 77.7k
28 votes
Accepted

An Infinitude of Deceptive Devourers

Answer: Explanation: Consider two possible cases. Case 1 - the children used the "at least" convention: Let's consider two subcases. Case 1a - only a finite number of people ate cake Case ...
Joseph Sible-Reinstate Monica's user avatar
28 votes

Interesting irrational number

Proof that the only positive solution is Let $y$ be a positive solution. Then Similarly, we can prove that is the only negative solution.
Evargalo's user avatar
  • 6,290
28 votes

Let's make a huge number with only tiny numbers

Using only addition, division, and decimal point magic, while preserving the order of the digits: Or alternately, using some sillier operators and a nifty coincidence: Or utilising combinatorics: ...
Bass's user avatar
  • 77.7k
28 votes
Accepted

How to solve 1 2 3 4 5 = 5 4 3 2 1 (insert five pluses to make it equal)? A thorough solution needed

Another way to think about it is to start with plus signs in all eight positions. The sums are equal at $15$. When you remove a plus sign you add
Ross Millikan's user avatar

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