dcowboys107 Posted December 4, 2005 Share Posted December 4, 2005 Jack Handley's new telephone number, together with the area code, forms a ten-digit number consisting of a pair of 1's separated by one digit, a pair of 2's separated by two digits, a pair of 3's and a pair of 4's both separated by three digits, and a pair of 5's separated by five digits. Neither the sixth nor the ninth digit is a 4. What is his new telephone number? Link to comment Share on other sites More sharing options...
elfstone Posted December 4, 2005 Share Posted December 4, 2005 Jack Handley's new telephone number' date=' together with the area code, forms a ten-digit number consisting of a pair of 1's separated by one digit, a pair of 2's separated by two digits, a pair of 3's and a pair of 4's both separated by three digits, and a pair of 5's separated by five digits. Neither the sixth nor the ninth digit is a 4. What is his new telephone number?[/quote'] It's 4352432151. Got there mostly by chance, the only calculation I did was assign x,y,z,w and k as the positions of the first 1,2,3,4 and 5 respectively. Then it's clear that the positions of the second 1,2,3,4 and 5 are x+2,y+3,z+4,w+4 and k+6 respectively. The sum of all the positions is 1+2+...+10=55, so we get that x+y+z+w+k=18. The first five positions that add to 18 are 1,2,3,4 and 8. I didn't know how to go on more formally from here so I tried a couple of combinations to arrive at the solution. Link to comment Share on other sites More sharing options...
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