175
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 ...
- 22.8k
153
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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
112
votes
109
votes
Accepted
86
votes
Accepted
78
votes
Accepted
74
votes
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)...
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71
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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:
- 16k
67
votes
67
votes
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63
votes
Accepted
62
votes
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60
votes
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56
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_{\...
- 753
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.
...
- 13.7k
54
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52
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49
votes
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:
- 7,119
47
votes
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47
votes
Accepted
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 ...
- 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:
- 5,502
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:
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43
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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 ...
- 9,411
43
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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 ...
- 18.6k
42
votes
Accepted
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)), ...
- 22.8k
40
votes
Only top scored, non community-wiki answers of a minimum length are eligible