Wednesday, 11 April 2007

A train leaves Chicago travelling at ...

Here is a challenge that you may try and solve while waiting for the live coverage from the SIO to start.

The following really occurred during this years O2C Doeberl Cup.
Round 4 started at 3:00 pm. At 4:05 pm a player approached me to tell me that the clock being used in his game was defective. It seemed that both clocks were going at once. Knowing that this was highly unlikely with DGT clocks I investigated. But he was correct. Indeed both clocks were going at the same time. It turns out that the clock had been set to Hourglass mode, rather than Fischer mode. In Hourglass mode, the time that is used by one player is added to the time available for the other player.
In the case of the game at hand the time for the White player read 1:19, while for the Black player it was 1:40. Each player had started with 1 hour and 30 minutes (1:30) and should have received 30s added to their time for each move they played (although in this case they hadn't). White had just played his 14th move.
The question to solve is: In fixing the problem, what times should I set on the clock for each player?


Jonathon said...

Without thinking about it tooo much.

White had taken 37.5 minutes of the time so far. Black 27.5.

This means that White should be on 90 minutes - 37.5, then +7 due to increments. So should have 59.5 minutes total.

Black should have 90 - 27.5 + 6.5 = 69 minutes.

Give or take a few seconds for the fact that White was -11 and Black was +10, so we had to be somewhere in that minute.

What DID you end up setting the times?!

Shaun Press said...

This answer is correct, although in practice there was some rounding error.
What I found interesting about this was that it was probably the first time I had to solve a set of simultaneous equations to do my job as a chess arbiter.