A telephone number has the form ABC-DEF-GHIJ, where each letter represents a different digit.
The digits in each part of the number are in decreasing order; that is, A > B > C,
D > E > F, and G > H > I > J.
Furthermore, D, E, and F are consecutive even digits; G, H, I, and J are consecutive odd digits;
and A + B + C = 9.
What is the telephone number?
Justify your answer.
Solution to the Problem:
The telephone number is 810 - 642 - 9753.The last four digits GHIJ are either 9753 or 7531, and the other odd digit (1 or 9) must be A, B, or C.
Since A + B + C = 9, that digit must be 1.
Thus the sum of the two even digits in ABC is 8.
DEF must be 864, 642, or 420, which respectively leave the pairs 2 and 0, 8 and 0, or 8 and 6, as the two even digits in DEF.
Only 8 and 0 has sum 8, so ABC is 810.
James Alarie sent in the following two solutions:
Does a listing of my program count as justification of the answer? Here it is: for ($A=2; $A<=9; $A++) { for ($B=1; $B<$A; $B++) { for ($C=0; $C<$B; $C++) { if ($A + $B + $C == 9) { for ($D=4; $D<=9; $D=$D+2) { if (($D != $A) && ($D != $B) && ($D != $C)) { $E=$D-2; if (($E != $A) && ($E != $B) && ($E != $C)) { $F=$E-2; if (($F != $A) && ($F != $B) && ($F != $C)) { for ($G=7; $G<=9; $G=$G+2) { if (($G != $A) && ($G != $B) && ($G != $C) && ($G != $D) && ($G != $E) && ($G != $F)) { $H=$G-2; if (($H != $A) && ($H != $B) && ($H != $C) && ($H != $D) && ($H != $E) && ($H != $F)) { $I=$H-2; if (($I != $A) && ($I != $B) && ($I != $C) && ($I != $D) && ($I != $E) && ($I != $F)) { $J=$I-2; if (($J != $A) && ($J != $B) && ($J != $C) && ($J != $D) && ($J != $E) && ($J != $F)) { print "$A$B$C-$D$E$F-$G$H$I$J\n"; } } } } } } } } } } } } } Now, I'm looking at this in a more logical manner. The DEF part can only be 420, 642, or 864, and the GHIJ part can only be 7531 or 9753. A quick pairing listing the missing digits gives: 420-7531 6,8,9 does not add to 9 642-7531 0,8,9 does not add to 9 864-7531 0,2,9 does not add to 9 420-9753 1,6,8 does not add to 9 642-9753 0,1,8 this one works 864-9753 0,1,2 does not add to 9 The answer is 810- 642-9753.
Correctly solved by:
1. Marivi Bungay-Domingo | Philippines |
2. James Alarie | Flint, Michigan |
3. Martin Round | Studley, Warwickshire, West Midlands, United Kingdom |
4. Alyx Wells |
Mountain View High School, Mountain View, Wyoming |
5. Kursat Guzey |
Birdville Independent School District, Haltom City, Texas |
6. Anna Tetzlaf and Eliza Sheffield | Tuscaloosa, Alabama |
7. David Day | Harlingen, Texas | 8. Randy Lerner |
Mundelein High School, Mundelein, Illinois |
9. Jim Hooker | Johnson City, Tennessee |
10. Brijesh Dave | Mumbai city, Maharashtra, India |
11. Adalene Thomas |
Mountain View High School, Mountain View, Wyoming |