175 votes

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 ...
Dr Xorile's user avatar
  • 22.8k
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, ...
alexwlchan's user avatar
  • 2,487
112 votes

3:3! It's a football score!

Does this count?
Yly's user avatar
  • 759
109 votes

3:3! It's a football score!

If you are allowed to use decimals, then
Cameron White's user avatar
86 votes

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

phenomist's user avatar
  • 13.6k
78 votes

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

Answer: How?
f'''s user avatar
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74 votes

Use the numbers 1-9 to equal 1150

Here's an answer which
Rosie F's user avatar
  • 8,299
73 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)...
Chris Cudmore's user avatar
71 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:
Dan Russell's user avatar
67 votes

3:3! It's a football score!

Another answer could be
dcfyj's user avatar
  • 7,756
67 votes

The Cucumber Paradox

I'm gonna say: Explanation:
votbear's user avatar
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63 votes

Correct way to add 22 to 4 to get given value

If you consider the numbers as Then
KoA's user avatar
  • 2,430
62 votes

Make e using 1, 2, 3, 4, 5, 6, 7, 8, 9

Parcly Taxel's user avatar
  • 6,996
60 votes

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

What about this where
hexomino's user avatar
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56 votes

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_{\...
theonlygusti's user avatar
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. ...
Weather Vane's user avatar
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54 votes

9-5=5? Matchstick problem

Another solution:
Scott Miller's user avatar
52 votes

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

No rules? Looks like 88 to me if I squint.
Andrew Morton's user avatar
49 votes

A truly amazing way of making the number 2016

JMP's user avatar
  • 35.6k
48 votes

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:
ManyPinkHats's user avatar
  • 7,119
47 votes

A truly amazing way of making the number 2016

And three more à la Perry
Pietro Majer's user avatar
47 votes

9-5=5? Matchstick problem

Here's one way: For the image-impaired:
tmpearce's user avatar
  • 4,100
47 votes

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 ...
Deusovi's user avatar
  • 145k
46 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
  • 5,502
45 votes

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:
Rauwyn's user avatar
  • 496
43 votes

How to get 5 from 0,0,0 and 1?

First off, latest edit - just for fun, how to get 5 from just 0 and 1: Before rule change posted: With the changed rules: And while we're at it, here's $0$ to $28$: And here's how to get 5 from ...
Paul Evans's user avatar
  • 9,411
43 votes

The computer can't do anything I couldn't do with pen and paper

Not sure if this counts as "pencil-and-paper" but certainly counts as "no computer..." $$ 3^{100} = 10^{100 \log 3} $$ We can compute this logarithm using a slide rule. The D and L ...
2012rcampion's user avatar
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42 votes

Is this sequence that hard?

Probably way over thinking this: There is a hint that: Reason:
p.s.w.g's user avatar
  • 861
42 votes

How do you get 23 using the numbers 1, 2, 3 and 5?

As stated the problem is not possible. Here's an online solver to show that. Lateral thinking options could fix it (like @Apep (reinterpretation of the list), @jlars62(decimal point (very clever)), ...
Dr Xorile's user avatar
  • 22.8k
40 votes

3:3! It's a football score!

The simplest one is:
KeyboardWielder's user avatar

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