Efficient Measures

Probability Level 1

Using one 2 meter length and two 3 meter length, I can measure 8 meters as shown in Figure 1. It is also possible to measure 1 meter, as shown in Figure 2. Which whole number length from 1 to 8 cannot be measured directly from one 2 meter length and two 3 meter length?


The answer is 7.

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Tan Chee Sen by Tan Chee Sen , 25, Malaysia

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7 solutions

Lucas Burgel
Jun 19, 2014

2 -> one 2 meter length
3 -> one 3 meter length
4 -> two 3 meter length "minus" one 2 meter length
5 -> one 2 meter length + one 3 meter length
6 ->two 3 meter length
So, 7 is the only one left!


13 Helpful 1 Interesting 0 Brilliant 0 Confused

Take the 2 from the 3 and that leaves one, then add both 3's back in and you get 7. The question doesn't state you can only use each piece one time.

Chris Fromer - 5 years, 4 months ago

how can we measure 4 m???

Gurjot Sodhi - 6 years, 8 months ago

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4 2 x 2 and x = 4

Aryan Gaikwad - 6 years, 3 months ago
Manos Kothris
Feb 4, 2016

We can also mesure 7 meters

Actually we can mesure all integer distances

8 Helpful 2 Interesting 5 Brilliant 2 Confused

How do you know how much space there is between the blocks in figure 2?

Calvin Lin Staff - 5 years, 4 months ago

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I moove the 2m block from figure 1, so it is 2m.

Manos Kothris - 5 years, 4 months ago

Yeah.. another way of getting the 7 is by removing the 2 metre length from figure 1 and replacing it with figure 2...

Nehemiah Osei - 5 years, 2 months ago

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Read the question. You do not have 2 2metre lengths to use.

Calvin Lin Staff - 5 years, 2 months ago

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Oops... sorry.. I forgot about that part. Lol

Nehemiah Osei - 5 years, 2 months ago

Clever answer here, but the question states that the distance is measured directly, and by moving the pieces during the measurement does not make a direct measurement.

D C - 4 years, 10 months ago

I got it!!!

renzo gantala - 3 years, 7 months ago

Yeah, if i can measure 1 meter i can measure every integer distance.

Martin Gütlbauer - 3 years, 6 months ago

I don't really understand the question, so can someone help me out on this, please? P.S. Sometime SOON.

mash religion - 3 years, 6 months ago

I got 7 as the correct answer guys.

Kamila Parveen - 2 years, 3 months ago
Noel Lo
Jul 17, 2015

1 = one 3 metre length minus one 2 metre length (3-2)
2 = one 2 m length
3 = one 3 mtre length
4 = two 3 m length minus one 2 metre length (2 3 - 2 = 6-2)
5 = one 2 metre length + one 3 metre length (2+3)
6 = two 3 metre length (2 3)

So 7 is the only one left

2 Helpful 0 Interesting 0 Brilliant 0 Confused

(3-2=1), 2, 3, (3+3-2=4), (3+2=5), (3+3=6), ......, (3+3+2=8). Hence 7 is the answer

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Sam Cheung
Jun 20, 2014

1 as shown

2 given

3 given

4 = 3+3-2

5=3+2

6=3+3

7 Not possible

8 as shown.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

yes,we have the same thinking!

Agustin Peñalosa Jr. - 6 years, 11 months ago
Theo Leinad
Jan 17, 2016

Actually it is possible to length 7: just length 5 units and replace rule 2 by 3, so you have measured 5 units and use the 2, to length the 7 units required.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

You can't use the 2 twice.

Calvin Lin Staff - 5 years, 4 months ago

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I'm not, I used 3+2 (replace the 2 for the 3 so you have 3+(3-1)= 5 and then use the same rule that lengths 2... 5+2

Theo Leinad - 5 years, 4 months ago

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You cannot "replace the 2 for the 3".

Calvin Lin Staff - 5 years, 4 months ago
Krishna Garg
Jun 20, 2014

With 2 MT and two of 3 Mts except 7 all other measures can be done since all other lenghs can be done by addition or substraction. So, Answer is 7. K.K.GARG,India

0 Helpful 0 Interesting 0 Brilliant 0 Confused

U can combine both the 3 meter lenghts and from the seond figure if we rotate the two meter block it comes a 4 meter measurment+3meter measurment...so 7 meter can also be measured

nik hil - 6 years, 11 months ago

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Yes ,that is possible by folding 2 meter to 2X1 Meter,good idea,Thanks Nik Hill,where are you from?

K.K.GARG.India.

Krishna Garg - 6 years, 11 months ago

Dude...you dont have a chalk to mark that 4 metres

Aman Kumar - 4 years, 1 month ago

We can measure 7..by two 3 mtr stick ryt.?

Arpan Modi - 6 years, 10 months ago

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