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## February 2020 Problems of the Month

### Problem A

Using the principle/pattern followed in grids A, B, C, and D, determine the numbers to be placed in the blank spaces of grids E, F, G, and H. In your comment, be sure to explain how you found your solution!

### Problem B

If we have a 3 x 5 rectangle on graph paper, diagonal of that rectangle crosses seven squares. Similarly, a diagonal of a 5 x 8 rectangle crosses twelve squares, and a diagonal of a 6 x 9 rectangle also crosses twelve squares.

Using the rectangles shown above as a guide, find a rule to predict the number of squares crossed in rectangles with the following dimensions:

a) 14 x 21
b) 15 x 22
c) 13 x 39
d) 29 x 38
e) 14 x 42
f) 48 x 55
g) 42 x 63

### Problem C

Suppose you have two buckets, one holding 5 liters and one holding 8 liters. Explain how to get the following measures of water (having access to as much water as needed):

a) 1 liter

b) 4 liters

### Problem D

In mathematics, the factorial (!) of an integer is the product of the positive integers less than or equal to it. So, for example, 4! = 4 x 3 x 2 x 1 and 9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

When its factors are multiplied and the product written in standard form, 9! = 362,880

The standard form of all factorials larger than 9, end in at least one zero.

Determine the number of zeros that appear at the end of 25! when written in standard form.

Determine the number of zeros that appear at the end of 100! when written in standard form if the prime factorization of 100! is…

297 x 348 x 524 x 716 x 119 x 137 x 175 x 195 x 234 x 293 x 313 x 372 x 412 x 432 x 472 x 53 x 59 x 61 x 67 x 71 x 73 x 79 x 83 x 89 x 97

Explain how you know!

All comments will be published at 8:00 PM on February 29, 2020.