Thank you very much

Only this munugget puzzle have this effect? Any other number that can have this effect also? Thank you for helping me.

the concept behind the puzzle is interesting, and as long as you can understand the concept, you can create infinite number of your own puzzles that has the same effect.

assume that we choose to have boxes of size X,Y,Z, where X is the smallest number of the 3 numbers

we consider the LCM of X & Y, and the largest no. of Y that we need is [ ((LCM of X & Y)/Y) - 1 ]

we consider the LCM of X & Z, and the largest no. of Z that we need is [ ((LCM of X & Z)/Z) - 1 ]

next, form different numbers N, with N = aY + bZ
where …
a < (LCM of X & Y)/Y
b < (LCM of X & Z)/Z
thereafter, any number N+X, N+2X, N+3X can be formed

for example, we can create a puzzle with box of size 10, 12 & 15
maximum no. of box of size 12 is 60/12-1 = 4
maximum no. of box of size 15 is 30/15-1 = 1

with a=0,b=0,
can have N = 10,20,30,40, …
with a=0,b=1,
can have N = 15,25,35,45, … cannot have N = 5
with a=1,b=0,
can have N = 12,22,32,42, … cannot have N = 2
with a=1,b=1,
can have N = 27,37,47,57, … cannot have N = 17,7
with a=2,b=0,
can have N = 24,34,44,54, … cannot have N = 14,4
with a=2,b=1,
can have N = 39,49,59, … cannot have N = 29,19,9
with a=3,b=0,
can have N = 36,46,56, … cannot have N = 26,16,6
with a=3,b=1,
can have N = 51,61,, … cannot have N = 41,31,21,11,1
with a=4,b=0,
can have N = 48,58,68, … cannot have N = 38,28,18,8
with a=4,b=1,
can have N = 63,73,, … cannot have N = 53,43,23,13,3

largest number that cannot be formed is 53

so, create your own puzzle and test your classmates :)

Oh, sound interesting. Math is challenging but kind of struggle too. Thank you very much for your clear explanation.

Thank you