To understand the notion of base numbers, we look at our own number system. We use the decimal, or base-10, number system. To help explain what this means, consider the number 2746. This number can be rewritten as
Note that each number in 2746 is actually just a placeholder which shows how many of a certain power of 10 there are. The first digit to the left of the decimal place (recall that the decimal place is to the right of the 6, i.e. 2746.0) tells us that there are six
1. You have a pan scale and weights weighing 1g, 3g, 9g, 27g and 81g (one of each). How to balance a 61g load on these scales? (weights can be placed on both scales)
2. How to distribute 31 pounds into five wallets so that any amount from 1 to 31 pounds can be given out without opening the wallets?
3. What is the smallest number of weights needed to be able to weigh any number of grams from 1 to 15 on a pan scale, if the weights can only be placed on one pan of the scale?
4. You have the right to make 4 kettlebells of any weight. What kind of weights will these be so that they can be used to weigh loads from 1 to 40 kg on a cup scale (the weights can be placed on both cups of the scale)? Can you select the weights of four weights this way if the weights can only be placed on one pan of the scale?
5. Given a bag of granulated sugar, a cup scale and a 1 g weight. Is it possible to measure 1 kg of sugar in 10 weighings?
6. One man had a basement lit by three electric bulbs. The switches for these light bulbs were located outside the basement, so by turning on any of the switches, the owner had to go down to the basement to see which light bulb was lit. One day he came up with a way to determine for each switch which light bulb it turns on by going to the basement exactly once. What is this method?
7. A three-digit number begins with the number 4. If you move it to the end of the number, you get a number that is 3/4 of the original. Find the original three-digit number.
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