Preschooler maths?

So basically this is what happens within a pre-school kid’s mind within five to ten minutes after looking at this lump of numbers…

 

[*spoiler alert*]

 

To solve this, we will have to first look into what a preschooler will know about Math.

 

First of all, considering that this lump of equations is genuinely meant for preschool kids, there shouldn’t be constituted of any complicated mathematical formulations (as in nothing post-preschool). Meaning, there shouldn’t be any fractions, ratios, remainder theorem, any change in the numeral system (as in switching from decimal to binary or unary) or any of that sort. As such, there should only be the most fundamental mathematical manipulations involved, namely addition, subtraction, and perhaps multiplication and division, though the latter two might be too advanced for preschoolers. Simply put, finger counting.

 

When considered in this manner, it appears the mathematical processes should be able to be performed with simple decimal counting with two hands (10 fingers) since the right hand side of the equations ranges from 0 to a maximum of 6, which is within the range of 10. If that is the case, then it can be seen that a simple sum of counting (or addition) is performed within each equations when calculated from the left hand side of the equation to the right hand side. Let’s bear that in mind for the time being.

 

If this is a simple mathematical process of counting, then the question becomes a lot simpler. The counting of what? Apparently, each digit of the 4-digit number on the left hand side of each equation represents a certain value that is counted on the right hand side of that equation, and this value is uniform throughout all the equations. If that is the case, then from 0 to 9 (10 numbers in total), what are the values of each number? For that, let’s first look into the sets of 4-digits with one unified digit number (as in numbers of 0000, 1111 and so on).

 

0000 = 4

1111 = 0

2222 = 0

3333 = 0

5555 = 0

6666 = 4

7777 = 0

9999 = 4

 

From this, it appears that for numbers 1, 2, 3, 5 and 7, the digit value is 0, and for 0, 6 and 9, the digit value is 1 (since the digit is repeated 4 times, the right hand side result should be divided by 4). This can be verified from other equations, such as 7111 = 0 (since 7 and 1 has 0 value each), 2172 = 0 (1, 2 and 7 has 0 value each), 7662 = 2 (2 and 7 has 0 value each, and 6 has the value of 1), and so on. With that, we can determine the value of 1, 2 and 5 in the set of digits (2581) that we are asked to count for (we can no longer call it a “number” because it doesn’t function as one, and the arrangement of the digits no longer matters). However, there still remains a problem. What about 8?

 

Apparently, the digits 4 and 8 are not among the set of uniform digits that is exemplified in the above. But of course, there are number sets of digits that contain the digit 8 on the left hand side. Let’s look at them.

 

8809 = 6

8193 = 3

8096 = 5

6855 = 3

9881 = 5

 

Assuming that the value of 8 is x, if we replace the numbers with their attached values and consider the equations under normal algebraic conditions, we will have …

 

x + x + 1 + 1 = 6

x + 0 + 1 + 0 = 3

x + 1 + 1 + 1 = 5

1 + x + 0 + 0 = 3

1 + x + x + 0 = 5And so,

 

x = (6 – 2)/2 = 2

x = 3 – 1 = 2

x = 5 – 3 = 2

x = 3 – 1 = 2

x = (5 – 1)/2 = 2

 

Therefore, the digit 8 has the value of 2.

 

So, what we have left is that 2581 = 0 + 0 + 2 + 0 = 2, and therefore 2 is the final answer.

 

If this is what goes through a typical preschooler (assumably aged 5), then either I have went through a hyper retarded childhood counting apples and oranges, or the education system is so advanced that preschoolers are required to be capable of connecting all these ideas within 5 minutes. Of course, there are two issues that I have to acknowledge. The first is that a preschooler will not (hopefully) be able to logically deduce all these in as much detail (and in a relevant language) as what I have just done. Secondly, considering the assumption of the epigraphical statement, and the nature of these counting processes, the nature of this question is actually to challenge the registered concept of numbers within our mind. For preschoolers, the ideas or concepts of number is not as strongly registered within the mind when compared with a typical adult. However, that idea is wholly based upon a false assumption of stubbornness of adults in terms of the concept of numbers. That is not exactly true for programmers in general. The reason being is that programmers have to deal with a lot of abstract numbers and numerical representations, to an extent that a number can denote a lot more than, well, a numerical value. As such, for a typical programmer, 10 minutes seems to be more than adequate for this type of questions if he has his mind set upon tackling the question.