I need help with a problem for math, can someone help me?

Question

Here's the problem.

How can the Egyptian god Anubis use his primitive (but accurate) scales exactly three times so that 100 grams of sand can be split into piles of 82 grams and 18 grams? The problem is that Anubis only has 2 gram and 5 gram weights.

Please answer for me :)

I have no clue at all.

Answer 1

Puzzling's answer is correct, but a little difficult to follow. Here it is with each step more clearly defined:

1. Measure 7 grams using 5+2 gram weights
2. Add 5+2 gram weights to the 7 grams of sand and measure another 14 grams of sand. Next, put the 14 grams of sand to the side. We need to add 4 grams of sand to it to get 18 and we have one more use of the scale.
3. Since we have 7 grams of sand on the scale, we leave the 2 gram weight with the sand and put the 5 gram weight on the other side, removing 4 grams of sand will even out the weights. Put this 4 grams with the 14 for a total of 18 grams, and add the remaining 3 grams of sand back into the original pile. Now we have two piles, one 82 grams and the other 18 grams.

The answer by luv_phy is also correct and it has the advantage of being simpler and easier to follow!

Answer 2

I assume you only have one weight of each type, otherwise this would be straight forward. Here's how you do it with just two weights:

FIRST WEIGHING:
He can measure out 7 grams of sand using both weights on one side and sand on the other. Total 7 grams.

SECOND WEIGHING:
Next he can add the weights to the 7 grams of sand and measure another 14 grams. This is a total of 21 grams. It seems like too much, but there is a way to remove 3 grams...

THIRD WEIGHING:
Now put 5 on one side and 2 on the other. Now add sand from the 21 grams until the scale balances. This will be 3 grams that he returns to the bigger pile, leaving 18 grams.

The final result is one pile of 82 grams and one of 18 grams.

Answer 3

um using 8 5-gram weights twice will get 80 grams of sand

using 1 2-gram weight will get 2 grams

the left over is 18 grams and you've used the scale 3 times.

Answer 4

PERHAPS
(i just thought of this)

1st
He used his scale to split his sand into 50g on each side.

2nd
He repeats this with one of the 50g pile, forming 25g piles of sand.

3rd
From a 25g pile, he transfers sand to his scale till it balances both his 2g n 5g weights tgt. So he would remove 7g of sand from tt 25 g pile.

And he gets his remaining 18g pile of sand, and the rest forms 82g