# Kids Write Letters To Santa (Logic Problem)

#### MrAl

Joined Jun 17, 2014
10,087
Hello there,

You guys seem to like logic problems so here is one for ya.

Intro:
In the weeks before Christmas, the six gifted Romberg children wrote their letters to Santa.
Each child, aged 6 to 11, made a request for a different electronic device.
Determine the device each child asked for as well as the age of each child respectively.
The ages are: 6,7,8,8,9,11.
The devices are: FET Set, Footswitch, Bulb, Power Resistor, Transistor, SP3T Switch.
The kids names are: John, Betty, Don, Letty, Lisa, Mark

The clues:
1. The youngest child, who is three years younger than Betty, asked for the Bulb.
2. Mark is two years older than the child that asked for the Power Resistor.
3. Lisa, who did not ask for the SP3T Switch or the Bulb, is two years older than Letty and three years younger than Mark.
4. The seven year old asked for the Transistor.
5. John asked for either the SP3T Switch or the FET Set, and his twin asked for the other.

#### jpanhalt

Joined Jan 18, 2008
11,087
Are the twins fraternal or maternal twins? Were they born on the same date?

#### MrAl

Joined Jun 17, 2014
10,087
Are the twins fraternal or maternal twins? Were they born on the same date?
Hi,

Well, i thought the two ages 8 and 8 would be self explanatory. Make sense?

#### jpanhalt

Joined Jan 18, 2008
11,087
Hi,

Well, i thought the two ages 8 and 8 would be self explanatory. Make sense?
No. Twins can be days apart in age (even longer in extreme circumstance). Most important, they are not always the same sex nor even the same father. Thus, any consecutive ages, e.g., 6,7; 7,8; etc., can be twins, while 8,8 may not be. This is the 21st century.

#### MrAl

Joined Jun 17, 2014
10,087
No. Twins can be days apart in age (even longer in extreme circumstance). Most important, they are not always the same sex nor even the same father. Thus, any consecutive ages, e.g., 6,7; 7,8; etc., can be twins, while 8,8 may not be. This is the 21st century.
Hello again and thanks for your question,

Well although that may be true, the problem statement nor the clues give you that information so what you are really asking me is to reveal part of the solution. My opinion would be to start out assuming that they are the same age because if they were not that would mean that we happened to have a problem where it happened to be on a day that fell right in between the birthdays of two of the children. If the so called twins where born 2 days apart and we just happened to be asking this question on day 1 but several years later, THEN they could be said to be of consecutive ages. However, the chances of that are 1 out of about 365 while the chances of us asking the question on any other day is about 364 out of 365.

So you be the judge. Do you want to assume they both have the same age, or take that 1 out of 365 chance that the question was asked on the most deceiving day of the year?
If you are not happy with that conclusion, i will in fact give out that part of the puzzle, but that would mean it gets easier for you to solve. So take your pick and let me know.

It's an interesting question no doubt, but this is a good time to see how heuristics work sometimes in problems of real life. The question then becomes could there be two solutions depending on how we view the twins age relationship. Again though, if you prefer to be told the answer to the twin question i will supply it but i think you would be cheating yourself a little.

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#### jpanhalt

Joined Jan 18, 2008
11,087
My solution. This appears to be a variation of the six houses, house colors, and cars puzzle. The version that was popular in Pittsburgh mid-1990's had an Audi TT as one option. I was tempted to get one, but never did. Too small to carry anything useful.

John

#### MrAl

Joined Jun 17, 2014
10,087
You have a whole lot of such Logic Puzzles here
https://www.brainzilla.com/logic/logic-grid/
Hi,

I had been into these kinds of puzzles over the years, mostly some 20 years ago when i was studying automated reasoning. I've also enjoyed doing them by hand. These days i usually work on more practical things, but i believe the kind of thinking required to solve these is a good exercise for learning to solve other types of problems in real life.

#### MrAl

Joined Jun 17, 2014
10,087
My solution. This appears to be a variation of the six houses, house colors, and cars puzzle. The version that was popular in Pittsburgh mid-1990's had an Audi TT as one option. I was tempted to get one, but never did. Too small to carry anything useful.

John
Hi again,

Yes that looks right
I would not doubt that these problems come out similar to other problems.