In the first hour, he sold one-half of his sticks, plus one-half of a stick. The next hour, he sold one-third of his remaining sticks plus one-third of a stick. In the third hour, he sold one-fourth of what he had left, plus three-fourths of a stick. The last hour, he sold one-fifth of the remaining sticks, plus one-fifth of a stick. He did not cut up any sticks to make these sales. He returned home with 19 sticks. How many did he originally take to the event?

Let x equal the number of sticks he started with. We have: The equation is 4/5 * (3/4 * (2/3 * (0.5x - 0.5) -1/3) - 0.75) - 0.2 = 19 Add 0.2 to each side: 4/5 * (3/4 * (2/3 * (0.5x - 0.5) -1/3) - 0.75) = 19.2 Multiply each side by 5/4 (3/4 * (2/3 * (0.5x - 0.5) - 1/3) - 0.75) = 24 Multiply the inside piece first: 2/6x - 2/6 - 1/3 2/6x - 4/6 Now subtract 0.75 which is 3/4 2/6x - 4/6 - 3/4 4/6 is 8/12 and 3/4 is 9/12, so we have: 2/6x - 17/12 Now multiply by 3/4 6/24x - 51/48 = 24 Simplify: 1/4x - 17/16 = 24 Multiply through by 4 x - 17/4 = 96 Since 17/4 = 4.25, add 4.25 to each side x = 100.25 Since he did not cut up any sticks, he has a full stick to start with: So x = 101

Ok. To go further in this equation. It reads: ...How many did he originally take to the event? Multiply the answer by 3 and reverse the digits. This will give you the answer for ACH in the coordinates. Does that make sense to reverse 303? :-/ Thank you for your help!!

Let x equal the number of sticks he started with. We have: The equation is 4/5 * (3/4 * (2/3 * (0.5x - 0.5) -1/3) - 0.75) - 0.2 = 19 Add 0.2 to each side: 4/5 * (3/4 * (2/3 * (0.5x - 0.5) -1/3) - 0.75) = 19.2 Multiply each side by 5/4 (3/4 * (2/3 * (0.5x - 0.5) - 1/3) - 0.75) = 24 Multiply the inside piece first: 2/6x - 2/6 - 1/3 2/6x - 4/6 Now subtract 0.75 which is 3/4 2/6x - 4/6 - 3/4 4/6 is 8/12 and 3/4 is 9/12, so we have: 2/6x - 17/12 Now multiply by 3/4 6/24x - 51/48 = 24 Simplify: 1/4x - 17/16 = 24 Multiply through by 4 x - 17/4 = 96 Since 17/4 = 4.25, add 4.25 to each side x = 100.25 Since he did not cut up any sticks, he has a full stick to start with: So x = 101

Let x equal the number of sticks he started with. We have: The equation is 4/5 * (3/4 * (2/3 * (0.5x - 0.5) -1/3) - 0.75) - 0.2 = 19 Add 0.2 to each side: 4/5 * (3/4 * (2/3 * (0.5x - 0.5) -1/3) - 0.75) = 19.2 Multiply each side by 5/4 (3/4 * (2/3 * (0.5x - 0.5) - 1/3) - 0.75) = 24 Multiply the inside piece first: 2/6x - 2/6 - 1/3 2/6x - 4/6 Now subtract 0.75 which is 3/4 2/6x - 4/6 - 3/4 4/6 is 8/12 and 3/4 is 9/12, so we have: 2/6x - 17/12 Now multiply by 3/4 6/24x - 51/48 = 24 Simplify: 1/4x - 17/16 = 24 Multiply through by 4 x - 17/4 = 96 Since 17/4 = 4.25, add 4.25 to each side x = 100.25 Since he did not cut up any sticks, he has a full stick to start with: So x = 101

Let me post the whole equation paragraph: Brainteaser # 1: Answer for ACH A fellow geocacher decided that he would try to sell some hand-made walking sticks at the local geocaching picnic event. In the first hour, he sold one-half of his sticks, plus one-half of a stick. The next hour, he sold one-third of his remaining sticks plus one-third of a stick. In the third hour, he sold one-fourth of what he had left, plus three-fourths of a stick. The last hour, he sold one-fifth of the remaining sticks, plus one-fifth of a stick. He did not cut up any sticks to make these sales. He returned home with 19 sticks. How many did he originally take to the event? Multiply the answer by 3 and reverse the digits. This will give you the answer for ACH in the coordinates. Make sure to multiply and reverse the digits. What would the answer be?

Multiply the answer by 3: 101 * 3 = 303 Reverse the digits: 303 reversed is a palindrome, so it's still 303.