`three pieces of `four

Hi,

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One morning Me, Iri and BGD were coming home after swimming. Cap of hot tee was long anticipated and we bought to it 3 peaces of `cremsnit (aka. Napoleon in U.S.).

Already far from backerei we realize - there 4 of us to share 3 peaces. How to share?

BGD suggest that we split each unit by 4, formally
Solution 1:

3u = 3 * 4 * u/4 = 4 * 3u/4  

I wanted extra unit for myself (irrational part of deal), than we can take module and split it even !
Solution 2:

|2u + i1u| = 1u + 2 * 2 * u/2 = 4 * u/2

Ups.. nobody liked my idea much.

Iri comes with another split where two pieces divided by half and one by four:
Solution 3:

2 * 2u/2 + 1 * 4u/4 = 4 * u/2 + 4 * u/4 = 4 * (u/2 + u/4) 

She argued that this fractal approach guaranty to work if we were N modulo 4:

N * (u/2 + u/4 + .. + u/N)

At the time of last solution we already finished tee.

I told kids folks tail about smart crow who helped divide cheese ball between two baby foxes. After initial split, ether fox wasn't happy with it piece so crow have to eat smaller one and start all over again. Eventually they reach atomic cheese unit. You can imagine how small it was but everybody left happy, including stomachached craw.

Kids agreed that crows solution was fare.
It makes me think about kind of education I provide to them.