24 votes
Accepted

Two-Move Chess Game

fblundun's user avatar
  • 1,367
24 votes
Accepted

$\pi$ = 13, $\sqrt{2}$ = 7, $e$ =?

I think the answer is Indeed, looking at $\pi=13$: $\sqrt{2}=7$: So:
Jujustum's user avatar
  • 548
14 votes

Which parent should you start playing against?

Mary should play the parent first.
Nuclear Hoagie's user avatar
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:
Nitrodon's user avatar
  • 229
8 votes

Which parent should you start playing against?

I'm going to go counter-intuitive and say...
Stevish's user avatar
  • 634
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
Vladimir Cravero's user avatar
5 votes

A Sierpiński Carpet ratio

This is the result: Here's my own reasoning:
Frank Soll's user avatar
5 votes

How to sell at the buying price and still have something in hand?

He probably just
Jujustum's user avatar
  • 548
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 ...
Albert.Lang's user avatar
  • 3,991
4 votes
Accepted

A Sierpiński Carpet ratio

A proof almost without words:
AxiomaticSystem's user avatar
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
quarague's user avatar
  • 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 ...
Stevish's user avatar
  • 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 ...
RobPratt's user avatar
  • 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.
Nuclear Hoagie's user avatar
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 ...
Sneftel's user avatar
  • 2,946
2 votes

A Sierpiński Carpet ratio

Here is a much simpler way of getting the same answer:
Orntt's user avatar
  • 281
1 vote

How to sell at the buying price and still have something in hand?

I think a possible solution is:
10010100102ohno's user avatar
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 ...
Falco's user avatar
  • 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 ...
computer_goblin's user avatar
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. ...
D S's user avatar
  • 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 ...
Prem's user avatar
  • 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 ...
Tim C's user avatar
  • 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) ...
AxiomaticSystem's user avatar

Only top scored, non community-wiki answers of a minimum length are eligible