Last week I did the 'Junior Maths Challenge' in UK (yr 8 or below) and I got stuck on one of the questions. I found out the answer to it, but I can't figure out how that is the answer. I realise that this is probably a very easy question, but could you explain as basically as possible? I would deeply appreciate it! Thankyou to all who help :)
The question:
Just William's cousin, Sweet William, has a rectangular block of fudge measuring 2 inches by 3 inches by 6 inches. He wants to cut the block up into cubes whose side lengths are whole numbers of inches. What is the smallest number of cubes he can obtain?
I thought that the answer was 36 (since I thought that the highest common factor is 1), but the real answer is 15.
2007-05-04 07:46:35 · 7 answers · asked by sings_the_sorrow 2 in Science & Mathematics ➔ Mathematics
You are assuming that all the cubes have to be the same size (in which case, you can only cut them into 1x1x1 cubes.)
But some of the cubes can be 2x2x2. In particular, you can cut the fudge into two rectangular blocks, 2x2x6 and 2x1x6.
That first part can be cut into 3 2x2x2 cubes.
The second can be cut into 12 1x1x1 cubes.
2007-05-04 07:55:19 · answer #1 · answered by thomasoa 5 · 4⤊ 0⤋
At first I thought 36 also, but I see it's asking for the smallest number of cubes not the biggest. 36 is the biggest number of cubes he could get.
Well, the biggest cube he can make is 2x2x2, since the smallest side is 2 inches. He can get three of those out of the big piece. Now you have a 1x2x6 block of fudge that has to be cut into 12 1x1x1 pieces. 12 + 3 is 15.
In order to get the biggest cube out of a rectangle, you must make it the size of the smallest side.
2007-05-04 08:00:28 · answer #2 · answered by soelo 5 · 0⤊ 0⤋
It is asking for the smallest number of cubes not largest number of cubes, which is 36.
To obtain 15, you'll 2x6 plane with 3" thickness. That will give you 3 2x2x2 cubes and 12 1x1x1 cubes for a total of 15.
2007-05-04 07:58:49 · answer #3 · answered by strong_perkasa 2 · 0⤊ 0⤋
if cube side=2 then 6/2=3 cubes
the other cubes side=1 6/1=6 2*6=12
12+3=15 cubes
Hint:
Base length side=2+1
base short side=2
height=6
count the cubes
2007-05-04 07:58:48 · answer #4 · answered by iyiogrenci 6 · 0⤊ 0⤋
I think your mistake was to assume that all the cubes would have to be of the same dimension. If you don't assume this then you could divide the fudge into 3 (2X2X2) cubes and 12 (1X1X1) cubes: for a total of 15 cubes.
2007-05-04 07:54:07 · answer #5 · answered by bruinfan 7 · 1⤊ 0⤋
yep,, 15... from the 2x3x6 fudge, u can make 3 2x2 cubes and 12 1x1 cubes whose total is 15 cubes..the problem did not state that the cubes should have uniform lengths.
2007-05-04 08:00:55 · answer #6 · answered by rÅvi 2 · 0⤊ 0⤋
There is no way 15 is the answer to that question.
2007-05-04 07:53:00 · answer #7 · answered by dunny456 2 · 0⤊ 2⤋