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Lotto Losers (Posted on 2007-04-23) Difficulty: 3 of 5
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?

See The Solution Submitted by Josie Faulkner    
Rating: 4.3000 (10 votes)

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Solution solution | Comment 5 of 9 |

There are only 6 squares between 2 and 49, so Charlie took these, as indicated by the C's below.

This leaves only 6 multiples of 7 for Penny, as 49 is now not available.

Only two stretches of 6 remain, 29-34 and 43-48, for Assaf and Vernon to take.

The primes that remain are 2, 3, 5, 11, 13, 17, 19, 23, 37 and 41. If 6 of these are to total 150, none of them can be 2, as that would mean 5 odd numbers would add to an even number. All six must be odd to add to an even number. The remaining nine primes add to 169, so three primes must be stricken from the list that add up to 19.  That would be 3, 5 and 11, leaving those primes that are 13 or higher to be Federico's choices.

There are only six numbers of 10 or less remaining for Dej Mar.

That leaves only six multiples of 3 for Brianjn.

The remaining numbers must be the ones selected: 11, 20, 22, 26, 38 and 40.

 2      D
 3      D
 4 C
 5      D
 6      D
 7  P
 8      D
 9 C
10      D 
11         selected
12       B
13     F
14  P
15       B
16 C
17     F
18       B
19     F
20         selected
21  P
22         selected
23     F
24       B
25 C
26         selected
27       B
28  P
29   AV
30   AV
31   AV
32   AV
33   AV
34   AV
35  P
36 C
37     F  
38         selected
39       B
40         selected
41     F
42  P
43   AV
44   AV
45   AV
46   AV
47   AV
48   AV
49 C

  Posted by Charlie on 2007-04-23 14:58:14
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