24
votes
Accepted
24
votes
Accepted
$\pi$ = 13, $\sqrt{2}$ = 7, $e$ =?
I think the answer is
Indeed, looking at
$\pi=13$:
$\sqrt{2}=7$:
So:
- 548
14
votes
12
votes
Which parent should you start playing against?
Mary should play her first game against
To prove this, notice that if $n$ were even,
For the case presented in the puzzle, with $n$ odd:
- 229
8
votes
7
votes
Accepted
How to sell at the buying price and still have something in hand?
I believe that
and therefore by the end of the day
he can then sell back all the cows
- 186
5
votes
5
votes
4
votes
Accepted
Irregularly Deposited Compound Interest
Observation: Let's for the moment assume we know the optimal number of transfers and need only optimise the timing. Freezing all but one transfer (#k, say) we find that its best timing $t_k$ only ...
- 3,991
4
votes
Accepted
3
votes
How to sell at the buying price and still have something in hand?
A lateral thinking solution could be achieved by
Depending on the weight of the cows
- 1,691
3
votes
Irregularly Deposited Compound Interest
Not sure if I'm right here, but this is my best solution.
First of all, in my solution:
So, with that, I came up with the following formula:
Since I wasn't able to think of a way to expand that ...
- 634
3
votes
Accepted
Nimber mnemonic combinatorial puzzle
There are 384 solutions. Here's one:
I used integer linear programming as follows. Let $$P=\{a, b, c, d, e, f, g, h, i, j, k, l, m, n, o\}$$ be the set of positions, where position $o$ must take ...
- 12k
3
votes
How to sell at the buying price and still have something in hand?
"5 for 2 coins" is a woefully underspecified bargain - it doesn't say what you're getting 5 of, nor does it state what the value of the 2 coins is.
- 4,499
2
votes
How to sell at the buying price and still have something in hand?
He bought cattle for 100 silver coins, but sold the cattle for 100 gold coins. Then he traded the 100 gold coins he'd received for a larger number of silver coins, and bought the rest of the cattle ...
- 2,946
2
votes
1
vote
How to sell at the buying price and still have something in hand?
I think a possible solution is:
- 768
1
vote
How to sell at the buying price and still have something in hand?
The farmer already had some cattle with him when he entered the market.
He bought big adult cows and sold young/small cows.
His profit was the difference in worth between his original small cows and ...
- 2,181
1
vote
Which parent should you start playing against?
Mary should play against the
This is because
In the context of this problem this explains why Mary should play against
Sorry for the not "mathematical proof" and more of a logic based ...
- 328
1
vote
Which parent should you start playing against?
We can prove this using the expected value. Assume Mary plays her mother first. Let $P_m$ be the probability of winning against her mother, and $P_f$ be the probability of winning against her father. ...
- 119
1
vote
Which parent should you start playing against?
I am giving 3 Solutions.
I think the third Solution ( which is listed in reverse order ) is what Peter Winkler wanted.
SOLUTION 3 :
Let us assume some values. We will later see that these values are ...
- 5,114
1
vote
Irregularly Deposited Compound Interest
My own solution
The following is the solution I had when I posted this puzzle. It loses to Albert.Lang's answer, but beats others.
First observation:
Second observation:
Third observation:
That ...
- 2,434
1
vote
Irregularly Deposited Compound Interest
Consider an interval, over which a newly-deposited balance of $b$ accrues an interest amount $i$.
Why?
Let's crunch some numbers!
And now, a simple program: invest(balance, interest rate, time) ...
- 8,249
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