Seven of our members at Perplexus decided to try their luck on the UK Lottery. They each chose six different numbers from 1 to 49. (None of them chose the same number.)

If all six numbers were drawn, they would win millions; if five of their numbers, plus the bonus came up, they would win a few hundred thousand.

Brianjn chose multiples of three.
Dej Mar's greatest number was ten.
Federico chose primes totalling 150.
Assaf and Vernon each chose six consecutive numbers, Assaf's being higher in value.
Penny chose multiples of seven.
Charlie chose square numbers.

Would you believe these unlucky punters failed to choose a single correct number (not even the bonus)?

If the bonus number was 1, which six numbers came up on the lottery?

The numbers that were drawn are: 11 20 22 26 38 40

This is figured out by eliminating what numbers have to be used by who:

Charlie has the squares, of which there are seven over the range. He did not get the Bonus however, so he's left with:

4 9 16 25 36 49

Next we look at Penny. She has multiples of seven, of which there are also seven. Since Charlie has taken 49, there are only six left:

7 14 21 28 35 42

Now we should look at Dej Mar. He chose all numbers ten and lower, and one of his numbers was 10. So, since Charlie has taken 4 and 9, and Penny took 7, the bonus being 1, That leaves six values that satisfy his selection:

2 3 5 6 8 10

Looking at Assaf and Vernon now. Taking into account the values that we know have already been taken, we can determine that the only two ranges of six consecutive numbers that haven't been interfered with are 29 - 34 and 43 - 48. Since Assaf has the higher values, we are left with:

Assaf --- 43 44 45 46 47 48
Vernon - 29 30 31 32 33 34

Brianjn has the last remaining multiples of three which are:

12 15 18 24 27 39

As for Federico (who made my favorite selection of the group), we look at the remaining prime numbers which are: 11 13 17 19 23 37 41. The last six of which add up to one-hundred fifty:

13 17 19 23 37 41

The bonus number has already been given to be 1, and so the last six remaining numbers that had to be drawn in the lottery are:

11  20  22  26  38  40

And there we have it ... the unlucky group chose all but the "lucky" numbers that we just found. I'd hate to play with those odds on my side!

Posted by Justin on 2007-04-23 14:40:41