## Brain-Teaser 452

**From The Sunday Times, 11th January 1970** [link]

Three dice, numbered from 1 to 6, each had 2 blue, 2 red and 2 white faces. No number appeared in the same colour twice.

When Bill threw the dice they totalled 14, showing 2 white faces and 1 red. A second throw showed each die the same colour as before, but each had a different number totalling 15. On one die Bill noticed two similarly coloured sides added to 9.

The telephone rang and Bill went to answer it, leaving little Tommy by himself, who then picked up one of the dice and painted a red face white and a white face red. He then threw the dice twice producing firstly 3 whites and then 3 reds, each throw showing one of the repainted sides.

Tommy totalled the 3 whites to 8 and the 3 reds to 7. Unfortunately, sums were not his strong point and though he sometimes got them right, quite often he was 1 out, and sometimes even 2 out. However, he was certain that the 3 whites totalled more than the 3 reds.

What numbers did Tommy repaint (1) red, and (2) white?

[teaser452]

## Jim Randell 10:55 pm

on16 February 2019 Permalink |This Python program runs in 370ms.

Run:[ @repl.it ]Solution:(1) Tommy repainted 3 to red, (2) and 4 to white.There is only one possible set of dice:

The throws for Bill, showing 2 white faces and 1 red:

Both die 1 and die 2 have white faces that sum to 9.

Tommy chooses die 1 and repaints 3 from white to red, and 4 from red to white, giving (with the repainted faces indicated in braces):

Tommy then throws 3 whites (totalling 6 to 10), and then 3 reds (totalling 5 to 9), the white total being more than the red total.

So Tommy’s calculation of 8 for the reds and 7 for the whites were both out by 2.

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