Nov 8, 2006

## Reasoning Skills Brain Teaser

By: Caroline Latham

**Puzzle:**

Marie, Claude, and Jean are in a competition. Here are their results:

- The youngest person received the least points.
- Claude got half of the points of the eldest.
- Jean received as many points as both others combined.

**Question:**

Who is the eldest ?

**The Brain Exercise:**

This puzzle uses planning and reasoning skills. You read the statements and then must develop a plan to solve the problem using your reasoning skills. These skills are found predominantly in your prefrontal cortex. This area of your brain is responsible for executive functions such as planning, structuring, and evaluating voluntary, goal-directed behavior, i.e., activities requiring the constant comparison of planned acts with the effects achieved.

If you’ve already got the puzzle figured out, click on the link below to find the answer.

**Solution:**

Start with statement #2 which tells us that Claude is not the eldest. So the eldest must be either Marie or Jean. Statement #3 tells us that Jean received the sum of the other two people’s points, and those point totals are not equal, per statement #1 (the youngest has less points than the other two). For Jean to be the eldest, Claude and Marie would each have half of the points of Jean has, but we know they can’t have the same amount of points. Therefore, Jean must have the most points, and Claude must be the youngest, but Marie is the eldest.

this does not make sense..

If the youngest person has least points

jean has the sum of equal points of the other two.. (claude has 1/2)

then, no person could be the youngest and jean would be eldest by common sense.

honestly who made this??

The puzzle says that Jean has as many points as the other two people combined, and those points are not equal given that the youngest person has the least amount of points.

Try it with Jean as the eldest. Say Jean has 10 points, then Claude must have 5 points, leaving Marie with 5 points. Then, there is no least amount of points and therefore, no youngest.

But what if Jean got the most points, Marie was the eldest, and Claude got half of MarieÃ¢â‚¬â„¢s points? Then it works. Say Marie got 10 points, then Claude got 5 points, and Jean got 15 points.

The eldest did not have to get the most points.

ItÃ¢â‚¬â„¢s tricky and tests your automated assumptions!

great fun! Nobody said that the competition was about points. Good reminder to read close.

Coen: that’s the spirit!

Pls i don’t get it.

Hello Jazz,

I was starting to write an answer but I cannot really improve Caroline’s…

Let’s start with “Claude got half of the points of the eldest.”

Given this, it is clear Claude is not the eldest. The 2 options now are Marie and Jean.

Now, to make things easier, why don’t you get pen & paper and imagine 2 scenarios, one with Jean as eldest, one with Marie as eldest? give real numbers. You will see that Jean cannot be the eldest and yet fulfill those 3 constraints, therefore the only answer can be Marie.

In any case, the real point here is to try!

For further explanation, let’s revert back from the solution and rephrase the 3 results.

From most points to least:

— Jean = 2x + x

— Marie (eldest) = 2x

— Claude (youngest) = x

- Based on the results as indicated by the puzzle, both results 1 and 2 point to Claude; therefore it can be combined and rephrased as:

“Claude is the youngest person with the least amount of points, which was half the amount of points of the eldest.”

Interesting website BTW. =)

Forgot to rephrase the 3rd result:

“Jean received as many points as both Marie and Claude combined”

I suspect some people may falsely associate the eldest with the most points to begin with, which may complicate the puzzle.

“Jean received as many points as both others combined.”

While to some, this sentence might imply:

j = c + m

(where the variable represents the number of points of the respective person)

To me, all says is:

j >= m + c

In which case, both Marie and Jean could be the eldest:

youngest: Marie with 1 point

middle: Claude with 2 points

eldest: Jean with 4 points

So either: I can’t understand English properly, there are two answers, or premise 3 is too ambiguous.

I’m disappointed in the educational system! Great puzzle. There is only ONE answer!

🙂

It should be specified that “least” and “eldest” means *strict inequality*.

Otherwise, j=c=m=0 is a solution, which doesn’t reveal information about age.

:0

Is it Jean?

Two

One

Jean us the eldest

It’s Jean.

j=c+m

nobody says that there was a set amount of point for these three people..so M can have any points in between C and J.

If M is the eldest ‘x’ points C has ‘x/2’ points so J has(j=m+c) x+ x/2 so Jean has more .. he is the eldest…

Claude and Marie can have the same age .

In that case she can have the same points as Claude and phare 2 is still true.

I see. Marie is definitely the eldest. It doesn’t say the eldest gets the most points. See if Claude gets half the points of the eldest, and marie is the eldest, Jean can have as much as both of them, example claude — 20, marie, 40, jean 60. jean = marie + claude, Claude = 20 = Youngest. Jean = 60 = Not oldest, but most points, Marie = 40 = 2x Claude = Eldest.

I dont see any possible solution that fits all the variables.

Yes Jean would logically be the elder:

“Jean received as many points as both others combined”

but if Claude’s points were half of Jeans”

“Claude got half of the points of the eldest”

Then Marie had to have the same number of points as Claude so the first line isn’t true:

“The youngest person received the least points”

it took time to realize but marie is definitely the oldest. lets say score was 105. c got half of the oldest. j got both combined. c=35. m=70. 35+70=(j)105