173 votes
Accepted

How can 64 = 65?

This is a famous physical puzzle that can be tied to the fibonacci series. To answer the question as posed, the issue is that the two slopes are different ($\frac25$ vs $\frac38$). Note that all ...
  • 22.4k
153 votes

How can 64 = 65?

The diagram is misleading, as it hides a gap in the middle of the second configuration. This is what we actually get if we rearrange the shapes in question. Notice that the diagonal “bows” slightly, ...
  • 2,487
113 votes

XOR - Is it possible to get a, b, c from a⊕b, b⊕c, a⊕c?

If you're given just a⊕b and b⊕c, then you can calculate ...
  • 1,448
112 votes

3:3! It's a football score!

Does this count?
  • 759
109 votes
Accepted

3:3! It's a football score!

If you are allowed to use decimals, then
93 votes

1 2 3 4 5 6 7 8 9 = 100

Note: This answer only applies prior to the edit that clarifies that the expression on the left must evaluate to 100, rather than simply the equation being true. If you allow exponents, you can get ...
85 votes
Accepted

The mother of all age-of-the-captain riddles

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78 votes
Accepted

How many consecutive positive integers can you make using exactly four instances of the digit '4'?

Answer: How?
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74 votes

Use the numbers 1-9 to equal 1150

Here's an answer which
  • 7,883
72 votes

4 Attempts to Guess a Number Between 1-15

Yes. Guess 1st set (1,3,5,7,9,11,13,15) -> If the number is in the set, write down 1 Guess 2nd set (2,3,6,7,10,11,14,15) -> If the number is in the set, write down 2 Guess 3rd set (4,5,6,7,12,13,14,15)...
70 votes

XOR - Is it possible to get a, b, c from a⊕b, b⊕c, a⊕c?

This is not possible. Consider the two cases where a, b and c are all true or all false. Now in both cases we have a⊕b = b⊕c = a⊕c = false And more generally, $(...
  • 13.4k
70 votes

3:3! It's a football score!

Since the puzzle oddly and specifically mentions the symbol for the square root, I used this: but rotated and reflected it giving:
  • 15.9k
67 votes
Accepted

1 2 3 4 5 6 7 8 9 = 100

I believe that this is the smallest:
  • 1,674
67 votes

3:3! It's a football score!

Another answer could be
  • 7,706
67 votes
Accepted

The Cucumber Paradox

I'm gonna say: Explanation:
  • 4,607
63 votes
Accepted

Correct way to add 22 to 4 to get given value

If you consider the numbers as Then
  • 2,430
59 votes
Accepted

Making π from 1 2 3 4 5 6 7 8 9

4 ops = 1.9934200404 points: Off by 0.00108199. 5 ops = 2.2864604146 points: Off by 0.0000340537. 6 ops = 2.7136051067 points: Off by only 0.000000266764(!) Now we can keep taking square roots ...
  • 2,405
59 votes
Accepted

Number 88 from the digits 2, 0, 1 and 7?

What about this where
  • 125k
58 votes
Accepted

Where is Jennifer's husband?

Let's define $J$=Jennifer and $D$=Douglas. The problem can be rewritten as: $J=D+21$ $J+6=5(D+6)$ According to my math, Douglas is $D=(-\frac{3}{4})$ years old, which means $-9$ months. ...
  • 12.5k
55 votes
Accepted

Create all numbers from 0-100 only using all of 1,2,3,4 and 5

Also, you can use any operation. Ok then. $\begin{array}{c|c} 0 & \log_{\frac1 2} \left( \log_{4!!-3} 5 \right) \\ 1 & \log_{\frac1 2} \left( \log_{4!!-3} \sqrt 5 \right) \\ 2 & \log_{\...
55 votes

4 Attempts to Guess a Number Between 1-15

A simple way is to pick the number $X$ which is half-way through the range and ask Is it less than $X$? From the answer you can discard either the lower half or the upper half of the range. ...
54 votes

9-5=5? Matchstick problem

Another solution:
52 votes

Number 88 from the digits 2, 0, 1 and 7?

No rules? Looks like 88 to me if I squint.
48 votes
Accepted

Doubling/tripling puzzle: make 1 from 1536 in as few steps as possible

As Jo has already shown, this can be accomplished in To help visualize this problem, we can imagine: Proving minimality:
  • 6,969
47 votes

A truly amazing way of making the number 2016

  • 35.4k
47 votes
Accepted

9-5=5? Matchstick problem

Here's one way: For the image-impaired:
  • 4,015
47 votes
Accepted

Why are all numbers from 1 to 2N covered by weights with powers of 3?

It helps to think about the scale not in terms of balancing two objects, but in terms of creating a weight difference between the two sides. (If you want to balance out an object, you simply put ...
  • 140k
46 votes
Accepted

Five loaves and the extra traveller

Such an old chestnut! Each of them eats 5/3 loaves. The first traveler contributes 3 loaves, eats 5/3 himself, and gives 4/3 to the extra traveler. The second traveler contributes 2 loaves, eats 5/3 ...
  • 44.8k
46 votes

Building a 2 mile runway on a 1x1 mile island

Build two straight runways side to side, 1 mile long each. Then, put a portal-conducting surface at the end of the first runway and another one at the beginning of the second one. Finally, use your ...
45 votes
Accepted

Can you explain these equations?

The equations are I don't really feel like calculating all of them, but for the first and second one: The edit history hint helped a lot with this one. Edit: For completeness here are all three:
  • 496

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