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# The slightly odd shovel of beach sand

## Question

At the beach last summer my grandson filled his yellow pail with sand.

He then scooped out a toy shovel full of sand with the intent to bury me.

At the point in time, how "odd" was his pail shovel?

1. His pail shovel was more likely than not to have an odd number of grains of sand.
2. His pail shovel was less likely than not to have an odd number of grains of sand.
3. His pail shovel was equally likely to have an even or odd number of grains of sand.
Edited by bonanova
Te inquire of the shovel, not the pail.

## 2 answers to this question

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Assuming neither the pail or the shovel is empty, it's more likely to be odd, since an even original number of grains n can give n/2 possible odd/odd splits and n/2-1 even/even splits.

If one could be empty and not the other, it's a 50/50 split (well, excluding the case of a single grain of sand originally).

If either could be empty, it's more likely to be even.

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Assuming neither the pail or the shovel is empty, it's more likely to be odd, since an even original number of grains n can give n/2 possible odd/odd splits and n/2-1 even/even splits.

If one could be empty and not the other, it's a 50/50 split (well, excluding the case of a single grain of sand originally).

If either could be empty, it's more likely to be even.

Your solution is better than my statement of the puzzle.

I meant, of course, to enquire as to the oddness of the grains in his shovel.

Before he buried me.

OP modified accordingly

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