Thursday, November 2, 2017

Simple Puzzle (Tin of Biscuits) - multiple approaches

I was sure they will crack this puzzle quickly, but I was more curious to know their multiple approaches.

"A tin full of biscuits weighs 5 kg 200 gm. The same tin half full of biscuits weighs 3 kg. Calculate the mass of empty tin."

Almost all of them were done in about a minute.

Give this problem a try before you read the solutions below.


Tanvi's approach:

I took one more tin half full of biscuits. So two half-filled tins weigh 6 kg. But a fully filled tin weighs 5 kg 200 gms. So the difference in these two weights corresponds to the weight of tin i.e. 800 gms.

Kanchan's approach:

I halved the weight of fully filled tin, thus leading to 2600 gms. Now, the other half filled tin weighs 3000 gms. So the difference 400 gms corresponds to half the weight of tin. So the tin weighs 800 gms.

Vaishnavi's approach:

She solved this algebraically. Let the weights of tin and fully filled biscuits be T and B gms resp.

T + B = 5200 ...... (1)
T + 0.5 B = 3000  ....... (2)
T + 0.5 (5200 - T) = 3000   .......... (from 1)
T + 2600 - 0.5 T = 3000
0.5 T = 400
T = 800

To this Rohit responded,

Look at your 1st and 2nd equations. We can clearly see that 0.5 B = 2200.  
Thus B = 4400 and hence T = 800

How did YOU solve this problem? Was your approach different than any of the above?

Which approach did you like the most?

How about trying this with your students/ children? Would love to know their approach :)

Thanks and Regards

PS: Students belong to marathi medium government school (class-7 and 8) based at Navi-Mumbai. To know more about their Maths Enrichment program, check this link:


  1. Use Rectangular bar diagram to split the parts and then solve

  2. I found the difference between the full tin and half full, which was 2.2 kg. That is the weight of half the biscuits. Double that to get 4.4 kg. Subtract the full amount from 5.2 to get 0.8 kg.