tricky maths question

2008-08-25 1:04 am

One hundred large boxes are placed on the table. Some of these boxes are
selected and into each of them 8 smaller boxes are placed. Then some of these smaller boxes are selected and into each of them 8 smaller boxes are placed.
This process is repeated a few times. At the end of this process there are
233 empty boxes altogether. How many boxes are there in total?

回答 (1)

keaneutd

2008-08-26 4:03 am

✔ 最佳答案

Total number = 252

For convenience, just call the boxes "Large", "Medium" and "Small" respectively

Assume among the 100 large boxes, x boxes are selected and 8 medium boxes are placed

Now we have:
(x) large boxes, each with 8 medium boxes inside
(100-x) large boxes with nothing inside

Assume among those x large boxes, y boxes are selected and 8 small boxes are placed inside each medium box

Now we have:
(y) large boxes, each with 8 medium boxes and 64 small boxes
(x-y) large boxes, each with 8 medium boxes (no small box)
(100-x) large boxes (no medium/small box)

Total number of empty boxes:
(100-x) + 8(x-y) + 64(y) = 233
=> 7(x+8y) = 133
=> x+8y = 19

Total number of boxes
= Total large + total medium + total small
= 100 + 8x + 64y
= 100 + 8(19)
= 252

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