GeekDad Puzzle of the Week: An AUSM Bonus – Solution

Congrats to James Matarese for correctly guessing our (fairly old from a world-protecting standpoint) heroes’ ages. James gets a $50 gift code to ThinkGeek! Check out the solution after the jump for your code for $10 off your next purchase of $30 or more at ThinkGeek.

Special thanks to ThinkGeek for providing our prizes!

It’s holiday bonus time at headquarters of the Affiliation of
Unbelievably Superpowered Metahumans (AUSM). Holiday bonuses are only doled out to the heroes who have not yet reached the age of 90 and whose birthday falls on Christmas day. Amazingly, Alphaman, Betadude,
Gammagal, Deltakid, and Epsilonimo all qualify!

Last Christmas, Epsilonimo was older than Gammagal by three times as much as she was older than Betadude, and Deltakid was 10 percent younger than Betadude and 20 percent older than Gammagal. The difference between the ages of Alphaman and Epsilonimo is the same as the difference between the ages of Deltakid and Gammagal (and in the same sense).

Find the heroes’ ages.

Solution

Per the facts:

a) (E – G) = 3(E – B)
b) D/B = 9/10
c) D/G = 6/5
d) A – E = D – G
e) Per a) 2E = 3B – G

D must be a multiple of 9 and of 6 and is thus a multiple of 18 (denoted as m(18)). B is thus m(20) and G is m(15)

B and G must be both odd or both even (2E must be even). But B cannot be odd so B and G are both even. B is m(40) and G is m(30), D is m(36).

If B is 80, G is 60, and D 72, then from e), 2E = 180 and E = 90. But none of the heroes has yet reached 90 so:

Betadude = 40
Gammagal = 30
Deltakid = 36
Epsilonimo = 45
Alphaman = 51

Puzzlers who use code GEEKPUZZLE will get $10 off of their next purchase of $30 or more at ThinkGeek!

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