## Math Brain Taser-Tell me our ages

A grandfather says the following:

- “My son has the same number of weeks as the number of days my grandson has”
- “I have the same number of years as the number of months my grandson has”
- “If you add our ages you have exactly 100 years”

“Can you tell me our ages?”

This is 2 of 3 that Suineg was kind enough to send in!

*Answer can be entered into comment section below*.

Wanted to also ask: what do you think about the new comment system? Would it be better if we put a timer on each puzzle, and this way at the end of 48-72 hrs, all submissions show? Or do you prefer to have answers show up immediately?

suineg| PUZZLE MASTER | Profile August 24th, 2010 - 7:04 amI think it would be good to have the timer, so that depending on the difficulty level of the problem you show the submissions after 48 hours or 72 hours, or if it is a problem sent by bilbao 144 hours is a good time frame right,because this gives you enough time to see, think and answer the question without peeking the answer and also you dont have to wait to long to see the answers, cool.

jerome_fb| Profile August 24th, 2010 - 7:15 amGrandson is 5, son is 35 (34.7), father is 60 (60.3)

Shawn| PUZZLE GRANDMASTER | Profile August 24th, 2010 - 8:46 amIf Gramps is 60 years old:

His son is 35 years old

His grandson is 5 years old

Grandson would be 60 months = 1825 days

Son would be 1825 weeks = 35 years (+ 5 weeks)

Bobo The Bear| PUZZLE MASTER | Profile August 24th, 2010 - 2:52 pmThe equation I came up with used x=number of days for grandson:

12x/365 + 7x/365 + x/365 = 100

20x = 100*365

x = 5*365

So the grandson is 5 yrs old.

Then the son is 35 yrs old.

And the man is 60 yrs old.

(It’s nice that the value of the constant 365 cancels out. It could just as easily be replaced with 365.25 to clear up any leap year related difficulties.)

Hendy| Profile August 26th, 2010 - 12:14 pm60, 35, 5

Days in a year is not a factor; it boils down to days in a week and months in a year. The focus is really on the grandson, not the grandfather as the problem is posed.

S = age of son’s son or grandson (a.k.a. Sonny)

D = age of son or Sonny’s dad (a.k.a. Daddy)

G = age of grandfather or Daddy’s father (a.k.a. Gramps)

7 S = D (days/week)

12 S = G (months/year)

12 S + 7 S + S = 100

20 S = 100 therefore S = 5

7 S = 35 = D

12 S = 60 = G

Hendy| Profile August 26th, 2010 - 12:32 pmBTW, is Taser a play on words versus Teaser, or just a typo? )

Shawn| PUZZLE GRANDMASTER | Profile August 26th, 2010 - 1:36 pmA brain taser could really ruin your day!

RK| Founder | Profile August 26th, 2010 - 8:57 pmTake that, Typo!

Hex| PUZZLE MASTER | Profile August 27th, 2010 - 1:37 amThe only pre-requisite is the assumption that the number of days is proportional to the number of years.

Grandfather: g

Son: s

Grandson: gs

Ws=Dgs -> Ds=7 x Dgs -> Ys=7 x Ygs

Yg=Mgs -> Yg=12 x Ygs

Yg+Ys+Ygs=100 -> 12Ygs + 7Ygs + Ygs = 100 -> 20 Ygs = 100

Ygs=5

Ys=35

Yg=60

Hex| PUZZLE MASTER | Profile August 27th, 2010 - 1:39 am@RK, As for the revealing of answers, I suggest that you assign a puzzle difficulty level to each new puzzle, where each level is preset to a certain time span after which the comments will be revealed automatically.

RK| Founder | Profile August 31st, 2010 - 10:29 pmYes, the answer is 5,35,60. Nice job on this one.

As for the commenting/answers- will go ahead an implement the timer idea. Programmer is already working on it!

gauravf| Profile July 29th, 2011 - 12:22 am:-(