maths dominoes problem?
A set of double-nine dominoes includes a total of 55 dominoes. Each domino is divided into two segments and each segment has a total of 0 to 9 dots. Each possible pair of numbers from 0 to 9 occurs exactly once in the set. What is the total number of dots on all the dominoes in the set.
Does anybody know how to do this?
Bearing in mind I have one minute per question and no calculator, could somebody give me the fastest possible route to work questions like these out please.
Thank you
Comments
495
The quickest way is probably:
Each "number" appears an equal number of times. The average number of dots on a segment is 4.5 (the mid point of 0 to 9), so the average total number of dots is 9 per dominoe. There are 55 dominoes so the total is 9x55 = 495
A more consistent way of dealing with these problems is:
Each number appears on exactly 10 dominoes, it appears twice on one of the dominoes, so each number appears on 11 segments. The total number of dots is therefore 11*(0+1+2+3+4+5+6+7+8+9). The sum of 1 up to n is n(n+1)/2 (a well known fact you should have memorized). So the total number of dots = 11*9*10/2 = 495.