A classic:
Rameses wishes to build a great pyramid for his interment.
The structure will have a square base and be solidly composed of cubical stone blocks. Each level of the pyramid contains one block fewer per side as the pyramid rises.
Rameses has available an initial work force of 35,000 slaves. Each morning the available labor pool is divided into work crews of 17 slaves each. Any remainder that cannot form a full crew gets the day off but are available the following day. Each crew can lay one block of the pyramid each day.
Unfortunately, the heat of the desert sun causes the death of one member of each crew each day. Work ceases on the project when it can be determined that there will be insufficient slaves available to raise the pyramid one more level. Each stone block measures 3 meters per side.
How many days will it take to construct Rameses' pyramid? How tall will it be? How many of the original slaves survive the construction?
(In reply to
re: answer by John)
Days to Complete: 53
Height: 138
Slaves Remaining: 2657
I misread my data, which resulted in a miscalculation of height by one layer. I also list my adjusted slave total based on an elevated understanding of the stop work aspect. All answers were generated by an Excel document. I used the following system if you wish to check my results:
A B C D E F G
1 35000 =INT(A1/17) =B137 =E1^2 1 =C1-C47 =B1
2 =A1-B1 =INT(A2/17) =C1-D1 =E2^2 2 =G1+B2
You should be able to simply drag the second line down to generate the sheet through line 136. If not directly write the next line and you can then drag the things. B137 should be =SUM(B1:B136)
Scrolling down to line 53 reveals that to be the point at which you have more blocks than F1 requires set. (F1 finds the total number needed.) G53-F1 gives the number of extra blocks, 73. This shows how many crews you did not need. A54 shows how many slaves were left if you used all crews on day 53. A54, 1416, plus 73*17 gives you 2657 unkilled workers. 46 was the last number to be squared and subtracted from your block total without giving a negative result. 46 is your height in blocks * 3m = 138m
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Posted by John
on 2004-11-06 00:52:26 |
re(2): answer
