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Lev Tolstoj's riddle

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A group of harvestmen was asked to scythe two fields. The first field was twice the size of the other. Half of the day the whole group worked on the bigger field, in the afternoon the group divided into half. First group finished the whole field by the end of the day. The second group went to scythe the smaller field and worked untill the end of the day too. However a small piece of this field was left undone. The following day the rest of the field was scythed. It took the whole day to finish it by one harvestman. How many harvestmen were in the group?

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8

here's why:

Say the fields are 6 acres and 3 acres,

and assume every man works at the same rate.

whole group did 2/3 of the 1st field [4 acres] the first morning.

half the group did the remainder [2 acres] the first afternoon.

It has to be 2/3 - 1/3 because the worker ratio was 2-1.

half the group did [again] 2 acres of the 2nd field in first afternoon

leaving 1 acre which required the entire second day for one man to do.

thus each man scythes 1 acre/day.

half the group did 2 acres in 1/2 day [4 acres/day] => 4 men.

whole group did 4 acres in 1/2 day [8 acres/day] => 8 men.

there were 8 men in the group.

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A group of harvestmen was asked to scythe two fields. The first field was twice the size of the other. Half of the day the whole group worked on the bigger field, in the afternoon the group divided into half. First group finished the whole field by the end of the day. The second group went to scythe the smaller field and worked untill the end of the day too. However a small piece of this field was left undone. The following day the rest of the field was scythed. It took the whole day to finish it by one harvestman. How many harvestmen were in the group?

im solving this as i go so bear with me:

split into three fields not two:

BBS

and just cuz i might need it, sextuple the letters to split fields up even more:

BBB BBB BBB BBB SSS SSS

Split first day into half-days

HD1: whole group does 2/3 of the B field or BBB BBB BB

HD2: half group does 1/3 of B field, or BBB B, which means the other half group must have done that much on the small field- SSS S, leavin SS to be done by one person in one day

So if one person does two parts...

the whole group did BBB BBB BB in half a day (half the time, so there's only ONE part per person)

so # of people = number of B's there

There are *counts* 8 workers

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This site is so cool. So I guess this puzzle has been on here a while but I am excited b/c I got the answer on my first try. so here goes:

The two fields; F1 and F2 (one is twice the size of the other)

F1 = 2*F2

The first day, first field was finished; (T= total number of people, D = day ie D/2 is half the day)

So T amount of people worked on the first field for half a day. Then half of T amount of people worked on the field for the other half of the day. This amount of work completed the field!

F1 = T*(D/2) + (T/2)*(D/2)

Second field:

Half the group worked for half a day and then one man worked for a full day. This amount of work completed the field:

F2 = (T/2)*(D/2) + 1*(D)

We know tht F1 = 2*F2 so you can set the equations equal to each other and with a little bit of algebra you conclude that there were 8 people. Great!

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A group of harvestmen was asked to scythe two fields. The first field was twice the size of the other. Half of the day the whole group worked on the bigger field, in the afternoon the group divided into half. First group finished the whole field by the end of the day. The second group went to scythe the smaller field and worked untill the end of the day too. However a small piece of this field was left undone. The following day the rest of the field was scythed. It took the whole day to finish it by one harvestman. How many harvestmen were in the group?

DO YOU MEAN LEO TOSTOY?

COZ I DONT KNOW LEV TOLSTOJ

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If the first field is completed at the end of the day, the full crew must have completed 66.6666666% of the large field. Leaving half the amount of the work that has been completed for half a crew to complete in the last half of the day. Finishing the first field.

This gives us the following statistics.

WHOLE CREW HALF DAY

66.6666666% large field

116.6666666% small field

WHOLE CREW WHOLE DAY

133.3333333% large fields

266.6666666% small fields

HALF CREW HALF DAY

33.3333333% large field

66.6666666% small field

Given the half crew can finish a 66.6666666% of a small field in a half day, on the second day the single man must have had to finish 33.3333333% of the small field in one full day. Being that a whole crew can finish 266.6666666% small fields in a full day it would take EIGHT men to accomplish this task.

My answer is 8

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A group of harvestmen was asked to scythe two fields. The first field was twice the size of the other. Half of the day the whole group worked on the bigger field, in the afternoon the group divided into half. First group finished the whole field by the end of the day. The second group went to scythe the smaller field and worked untill the end of the day too. However a small piece of this field was left undone. The following day the rest of the field was scythed. It took the whole day to finish it by one harvestman. How many harvestmen were in the group?

I like this one (probably cause I got the answer quickly).

Then entire group is able to finish 2/3rds of the larger field in half a day. Logically, half of them would finish 2/3rds of the smaller field in half a day. It takes 1 person twice the time to finish half the amount of work. So there must have been 4 people working on the smaller field. Since they represent half of the group, the group must be 8 harvestmen.

I know i skipped some steps in the logic, but it should make sense to someone who is close to or has found the solution.

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Let f represent the size of the smaller field (1/2 the bigger field).

Let g represent 1/2 the size of the group.

Let w represent the amount of work 1 harvestman can do in 1/2 day.

Then the big field (2f) takes 2gw + gw, or 3gw.

The small field (f) takes gw + 2w.

Multiply the work for the smaller field by two, to equal the amount of work for the big field, and we have:

3gw = 2gw + 4w. (subtract 2gw from both..)

gw = 4w. (divide both by 4...)

g = 4

Since g represents 1/2 the size of the group, there were 8 harvestmen.

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