My Son's Yr7 Maths Question

[xenou]

6298 has been excluded (see my post #7) so I'm still going with one solution.

ξ

 

[steve case]

... both 6298 and 8104 are valid solutions.

I got 8104 rather quickly, didn't try for number 2. You don't really need Excel for this one.

Part of it is understanding what the question is.

 

[xenou]

No formulas were harmed in the making of this thread.
ξ

 

[sundarrd]

I encountered the same situation
reading the question again and again
Each time two of the numbers are correct, and two are wrong. Can you work out the four digits of the PIN, in their correct order?"
The answer is NO
reason being as soon we read the question we try to find the pin and not pay real attention to what is being asked.
The answer to this is NO because 6298 and 8104 are one of the possible combinations.

even 4108 will fit all the 4 combination and it could be the correct order .
there are 24 combinations of this number 4 factorial

for example 8104 can be written as the following 24 combinations

8104, 8140, 8014, 8041, 8410, 8401, 1804, 1840, 1084, 1048, 1480, 8408, 0814, 0841, 0184, 0148, 0481, 0418, 4810, 4801, 4180, 4108, 4081, 4018

Revisiting the attempts:
6204
6108
8208
8198

as you can see with any number out of the 24 2 digits match in each instance.



same applies for 6298

so we have 48 numbers out of which 8104 and 6298 are two combinations.
so finding the correct order is not possible.

 

[xenou]

Each time two of the numbers are correct: I think that should be taken to mean that the digits are correct *and* in the right place.

Edit, however, I agree that the problem is cooked since 8014 and 6298 are both pins that would satisfy the original statement that "each time two of the numbers are correct and two are not"