Photo:
THE MIRROR
Marvin's ten tiles are numbered from 0 to 9. Unfortunately, the six-year-old lost one of the tiles.
He doesn't know what that is.
His mother knows that Marvin likes to solve puzzles and is already very good at arithmetic.
She asks him the following questions:
"Can you divide the nine stones into three groups so that the sum of the numbers in each of the three groups is the same?"
"Yes," Marvin replies.
"And does such a division also work with four groups, so that the sum of the numbers in each of the four groups is the same?"
"Yes, that works too," says Marvin.
"Now I know which stone you lost," says the mother.
Do you know?
Marvin lost the
number 9
stone .
The sum of the numbers on the nine remaining tiles must be divisible by 3.
Otherwise they could not be divided into three groups, each with the same sum.
The same applies: The sum of the numbers on the nine stones must be divisible by 4.
Both help us to find the solution.
Let's start with 3: the sum of the numbers on all ten tiles is 45. This number is divisible by 3.
Because the total is also divisible by 3 if a tile is missing, the missing tile must have a number that is divisible by 3.
So it must be one of the stones 0, 3, 6, 9.
Regarding 4: If one of the stones 0, 3 or 6 is missing, the sum of all other numbers is not divisible by 4.
If the stone with the number 9 is missing, division by 4 works.
Therefore, if there is a solution, only the number 9 stone can be the missing one.
However, we still have to check whether the nine stones can actually be divided into three and four groups.
This actually works in both cases, as the following breakdowns show:
Three groups with a total of 12 each:
(0, 4, 8), (1, 5, 6), (2, 3, 7)
Four groups with a total of 9 each:
(0, 1, 8), (2, 7), (3, 6), (4, 5)
I discovered this puzzle in the book "The Garden of the Sphinx" by Pierre Berloquin.
In case you missed a mystery from the past few weeks, here are the most recent episodes:
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All A's
A card makes the difference
The domino duel
Fairness at the coffee table
Magical 45
Perfectly arranged
Can these calculations add up?
Five points, three angles
Amazing exchange of digits