Virtual Two Pan Balance
This is pretty simple to figure out, but when the instructions are as simple as those below, it doesn't hurt you to read them. BTW, the images below are just to point you in the right spot, they deliberately don't zoom to a bigger picture. When you are ready, click on the picture of the two pan balance to the left to open up the application. |
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Choose items from the collection at the top. |
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Drag them onto the pans. |
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If the balance tilts, then one side is heavier than the other. Adjust accordingly. |
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You can zoom in on the needle by mousing over it, but it is deliberately without numbers. It is easiest to see from the tilt alone, which side is heavier. |
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There is a special adjustable mass that you can set to work the puzzles. The red up and down arrows above it allow you to change its mass from 0 to 64 even if it is already on the scale. |
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There is a set of red-ish masses that increase by factors of 2: 1, 2, 4, 8, 16, 32. Judicious use of these will permit you to weigh an integer mass from 0 to 64 inclusive. A corresponding mystery mass will be assigned a random integer value in the 0 to 64 range each time it is picked up. These binary-space-spanning masses are deliberately designed to only operate on the right pan. Here is a pdf file of a convenient chart for recording answers to this puzzle. |
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For a greater challenge, there is a set of four masses that increase by factors of 3: 1, 3, 9, 27. Clever use of these masses will permit you to measure all objects for which the integer mass is between 0 and 40 inclusive. The corresponding mystery mass and these four measuring masses are tinted slightly blue. Here is a pdf file that will help when doing this problem. Just to re-iterate. It ***IS*** possible to represent all the integer masses between 0 to 40 inclusive using only these four blue-ish masses. |
