What is the first resort of a child unable to finish his/her homework? The internet! However, at times, even the Internet can be stumped by a really tough question and may end up confused.

The latest puzzling problem came from a 10-year-old student of the fifth grade. The student from Glossop, England was confused by an elementary Math problem and he asked his grandmother for assistance. When she failed to solve it, the dad of the school kid posted the problem via his Facebook account to crowdsource the solution. Understandably, the problem went viral.

The viral story was picked up by the Manchester Evening News, who tweeted the Math problem with a request for help. After much head banging, an answer was found eventually.

In fact, the problem is basic geometry and is not much difficult at all. The source of difficulty is something quite different.

Matthew Zaremsky, a Professor of Math at the Binghamton University explains the solution.

## Question 1

Let’s start at the top of the figure and name this side as a. go clockwise naming the other sides accordingly in alphabetical fashion.

Since e and f are 10cm and 12cm respectively, while a + c equal 10cm and b + d equate 12 cm; thus, the total perimeter may be written as a + b+ c+ d+ e+ f which is the same as ( a+ c ) + ( b + d) + e + f = 10 + 12 + 10 + 12 = 44cm.

## Question 2

Just like the previous question, start at the top left corner, and move in clockwise direction naming all the edges. Thus, the perimeter equation comes out to be a + b + c + d + e + f + g + h. it may be rewritten as: a + b + ( c + e + g ) + ( d + h + f ) + 2f = 9 + 11 + 9 + 11 + 4 =44 cm.

The real source of difficulty in this question is not the problem itself , rather it is the label depicting the side of 2cm that stumped a lot of people. It is not clear that which side the label of 2cm is referring to. Although, it appears to be associated with side e but actually it refers to the measurement of the edge f. As Zaremsky explained:

“[The label] has to be labeling the side to its left for the problem to be doable. If it’s labeling (e), there’s no way to uniquely solve this. I think that ambiguous label is the only thing making this a ‘bad’ problem — but yeah, it’s definitely pretty hard for a 10-year-old.”

How long did you take to figure out the right answer?

## Comments 11

15 seconds

It should be (d + h – f), not (d + h + f).

We know that d + h – f = 11. But we don’t know and cannot find the value of d + h + f.

In addition, there is just one f in the perimeter, but in “a + b + ( c + e + g) + (d+ h + f) + 2f” statement, we have three f’s, which is not what we’re looking for.

For second question correct statement would be a+b+(c+g+e)+(d+h+f)=9+11+9+(11-f+f)= 30 as h+d-f=11 thereby h+d=11-f

Mahesh dwivedi is correct. In problem 2, the solution should be a+b+(c+e+g)+(d-f+h)+2f to become 9+11+9+11+2×2. Reason: d+h=11+f or 13.

I think for 2nd question :

f= 2cm

a =9 cm,

c+g+e =9cm,

b=11cm,

[(d-f)+(h-f)]=11cm.

[(d-2)+(h-2)]=11 cm

d+h=15cm

Then, a+(c+g+e)+b+(d+h)+f= 9+9+11+15+2=46 cm

Revised :

f= 2cm

a =9 cm,

c+g+e =9cm,

b=11cm,

[(d-f)+(h-f)]+f=11cm.

[(d-2)+(h-2)]+2=11 cm

d+h=13cm

Then, a+(c+g+e)+b+(d+h)+f= 9+9+11+13+2=44 cm

Question no 2 answer is wrong according to that calculation. It should be-2f not +2f

44

I solve it in 2mins according to the timer

Here’s a mistake in ans. no. 2 (d+h+f)=11, which is (d+h-f)=11

In second picture, I think it shuld be (h-f+d) or (d-f+h) not (h+f+d) as explained.