# Tag Info

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. ...
• 18.9k
Accepted

• 7,281

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

Same answer as PDT, just explained differently:
• 12.1k

### 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:
• 6,043
Accepted

### A colorful dodecahedron

Partial Answer: Solution: Other Solutions: Fun Stuff:
• 8,226
Accepted

### A strange operator on my new calculator

I think the operation replacing + is Examples Finally the last result produces an error because In fact
• 137k

### 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
• 3,770

### 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 ...
• 2,046
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.
• 753
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?" ...
• 15.4k

### 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:
• 6,185
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:
• 1,345
Accepted

### 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 ...
• 53.7k

### 2 vs. 1.005^200

This is quite easy if you know or The largest of the two numbers is
• 53.7k

### How many dogs of Oxford are there?

The smallest possible number of dogs is
• 2,924

### 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, ...
• 21.3k
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
• 7,281

### 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 ...
• 1,445
Accepted

### It's what's within the two

The answer to the puzzle is Which we must use to solve it!

### Make 27 using 1, 1, 1, 1

$3/(1/9)=$
• 821

### 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.

### 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.
• 14.5k
Accepted

• 3,326
Accepted

• 12.9k
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 ...
• 77.7k
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 ...

### 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.
• 6,290

### 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: ...
• 77.7k
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