Monday 8 February 2010

PUZZLE #3 SECOND LEG

PUZZLE #3 (from the 9th to the 24th of February 2010)

A WICKED FRIEND

James asked Sharon what her telephone number was. Sharon, who is very fond of Mathematics, answered this:“It is the only 9-digit number whose digits are all different and different from zero and in which ANY two consecutive digits make a number which is divisible either by 7 or by 13.
 Well, what’s Sharon’s telephone number?

SOLUTION 
We've received 5 correct solutions from:
Zsofia Zentai (Hungary)
Reka Vass (Hungary)
Máté Fenyvesi (Hungary)
Kristynna Mandá ková ( Czech Republic)
Joan Josep Pla (Spain) 
Luisa Wiechert (Germany)
Julian Kaping (Germany).


Here, we plublish Zsofia Zentia's solution

At first, we need to find all those 2-digit numbers that are divisible by 7 or 13.
ð  Numbers that are divisible by 7:
o   14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91 and 98.
ð  Numbers that are divisible by 13:
o   13, 26, 39, 52, 65, 78 and 91.
After a little observation we find that:
ð  Neither of these numbers ends by 7à the telephone number may start with 78
ð  Only number 4 can follow number 8. à784
Two numbers can follow 4: number 2 or 9.
3rd number of the phone number
4th
5th
6th
7th
8th
9th
4
2
8

4
2
1
4

4
2
1
3
5
6
3
4
2
1
3
5
6
5
4
2
1
3
5
2

4
2
1
3
9
8

4
2
1
3
9
1

4
2
6
3
5
6

4
2
6
3
5
2

4
2
6
3
9
1
4
4
2
6
3
9
1
3
4
2
6
3
9
8

4
2
6
5
6

4
2
6
5
2

4
9
8

4
9
1
4

4
9
1
3
9

4
9
1
3
5
6
3
4
9
1
3
5
6
5
4
9
1
3
5
2
1
4
9
1
3
5
2
8
4
9
1
3
5
2
6
So Sharon’s phone number is: 784913526.




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