Trolley conundrum

Mastermind conundrum

My kids are now of the age where they enjoy playing Mastermind. It has been agreed that the code-setter will always use four different colours, rather than the more sneaky version where the code-setter is allowed to use two or more of the same colour.

If you use one of each colour, then logically, the 'score' (the little red and white pegs) would be the same, whether you mark the guess on the basis of the answer or vice versa, because each coloured peg only counts once, for example:

Code: Re-Gr-Bl-Ye
Guess: Pu-Pi-Re-Ye

If the code setter marks the guess on the basis of the code, the purple and pink score nothing, the red scores a little white peg and the yellow scores a little red peg.

If the code-setter marks the code on the basis of the guess, the green and blue score nothing, the red scores a little white peg and the yellow scores a little red peg.

So we get the same mark either way - a little red peg and a little white peg. So far so good.
-----------------------------------------
Question: does this reciprocity hold if the code-setter is allowed to use two or more of the same colour? For example:

Code: Re-Gr-Rl-Ye
Guess: Pu-Pi-Ye-Bl

The purple, pink and blue score nothing, leaving a yellow, which scores a little white peg.

Now, with the same code, how do you mark...

Guess: Pu-Pi-Ye-Ye?

The purple and pink score nothing, there's one yellow in the correct place, which scores a little red peg, but what about the other yellow peg? In the absence of the correct yellow peg, it would have scored a little white peg. Some sort of logic and fairness says it gets nothing, because the yellow in the code has been 'used up'.

Further, if you were to mark the code according to the guess, you'd get the same result, the yellow in the code is in the 'correct' position, so that's one little red peg and the two reds and the green score nothing.

So, that's the question: if you are playing the sneaky version where the code setter is allowed to use the same colour more than once, can you ever have a code/guess combination where marking the code would give a different result to marking the answer?

Doesn't make sense

A headline in The Metro reads Couple forced to live in tent after removal van explodes on the M5.

The article explains how the removal van burned all their stuff "while they were moving house", but it does not explain why they couldn't move into their new house, even if they had to start buying furniture from scratch. It says that they had given up the lease on their old flat (so they can't move back in their) but not why the incineration of their stuff caused them to lose their new home and force them to camp in a relative's garden.

Hmm. Is it possible that there is no connection between the two events? That they were just evicted (or did a bunk) from their old flat?

Residential land values - USA

There was an intriguing article in the weekend FT on US residential land values. To cut a long story, values have fallen (and food prices risen), so developers are selling their land banks back to farmers (at a huge book loss).

But look at the figures involved:
Lakewood homes, a small mid-western builder, sold 290 acres of land in the Chicago suburb of Newark at $9,650 (€6,086, £4,831)) an acre in April, nearly 40 per cent below the $15,865 an acre the company paid for the land in November 2005, to a local agricultural investor.

Assuming that Newark is a typical sort of town, even £8,000 per acre is considerably less than one per cent of the average price/value of residential land in England/Wales, which had reached about £1,200,000 per acre in January 2008.

"Sure", I hear you cry, "but the US is a big country - we have a land shortage in the UK".

Well, yes and no. The UK is more densely populated, but don't forget that in either country, most of the population lives in urban or suburban areas - and what you are paying for when you buy a house is proximity to the nearest town, because you need access to jobs, schools, shops, hospitals etc.

Further, according to the Case Schiller Index, Chicago house prices are down by about 10% over the last two years. In the UK, the maths is simple: house price = bricks and mortar plus land value. In the 1990s crash, UK house prices fell by a third (in real terms) but land values (being a balancing figure) fell by two-thirds (in real terms).

But the typical price for a house in Newark appears to be about $300,000. If prices have fallen by 10% and land values were only $1,600 per residential plot at the peak, and assuming that such land cannot have a negative value, what's the balancing figure? Where did the other $30,000 fall in value go?