Fractions to Decimals

November 20th POW Answer

Solution: May and June.

To see how this works, all you need to know is that months with 30 days push the first of the month ahead two days of the week, whereas months with 31 days push ahead three days. For example, March has 31 days, so if March 1 is a Tuesday, then April 1 is a Friday (move ahead three days of the week). Similarly, April has 30 days, so May 1 will be a Sunday (move ahead just two days of the week).

The table below summarizes what will happen in leap and non‐leap years. August does not share the same day with any other month in a non‐leap year, and October does not share the same day with any other month in a leap year — but only May and June never share the same day of the week with any other months, whether it’s a leap year or not. Month	Months with Same First Day in a Non‐Leap Year	Months with Same First Day in a Leap Year
January	October	April, July
February	March, November	August
March	February, November	November
April	July	January, July
May	None	None
June	None	None
July	April	January, April
August	None	February
September	December	December
October	January	None
November	February, March	March
December	September	September

November 13th POW Answer

Solution:  532. 
Because we want the largest result possible, you should try to do two things: make the denominator of the fraction as small as possible, and make the numerator as large as possible.
To make the denominator as small as possible, you can use subtraction and division. The smallest possible denominator can be obtained with 1 – 8 ÷ 9, which has a value of 1/9, and
dividing by 1/9 is the same as multiplying by 9. That’s a good start. Then, to make the numerator as large as possible, take the three greatest remaining digits 5, 6, and 7, and combine them with the remaining operations, + and ×. The largest expression that can be formed in the numerator using these digits and operations is 6 × 7 + 5. Luckily, the result with this numerator and denominator contains the remaining three digits, 2, 3, and 4.


This is a very good answer, and if this is the answer you obtained, you should be very proud!
However, there is a better answer. If you compromise just a little on the size of the denominator, you can increase the size of the numerator, which will yield a greater result. In the denominator, use 1 – 6 ÷ 7, which has a value of 1/7. Dividing by 1/7 is the same as multiplying by 7, which isn’t as good as multiplying by 9, but it’s still pretty good. The benefit of doing this is that it leaves the largest digits, 8 and 9, to be used in the numerator. You can then make the expression 8 × 9 + 4 for the numerator, which will yield a final result on the right containing the digits 2, 3, and 5 that is greater than 423.

November 5th POW Answer

You would need to pull 48 candies!