GCXX3H - SirCumference's Challenge
By: Mathman, SirCumference, The Better Half, & Cutie Pi
1. Here is the puzzle.
Stage 1 is located at the following coordinates:
N 44° 54.AAA’ W 089° 32. BBC
SirCumference earned $9 working in the dunk tank at the Weston Metropolis Fair...
He stopped at Target to buy a pack of post-it notes, which cost him one third of his earnings for the day..
He ran over to Pick ‘N’ Save to check out the candy sales...A sign posted said that seven Gumdrops cost as much as two Snickers bars...
If SirCumference bought seven snickers bars and 13 gumdrops, he would spend 1/4 of the amount he did for the post-it-notes at Target...
He was extra hungry and bought 14 Snickers bars and 11 gumdrops...
How much of the $9 did SirCumference have left after buying the post-it-notes, snickers bars, and gumdrops?
The Better Half decided to host a CITO event from 5:00-8:00 p.m on October 4, 2006. She spent half of her budget on the Brats, Buns, and Chips for the 50 people attending...
She then bought drinks, costing half of what she had left, plus $10 more...
Knowing that picking up garbage for the CITO could get messy; she picked up paper towels and hand sanitizer, which cost half of her remaining money, and another $10 on top of that...
After hoping she could buy herself an old GPS with the remaining money, she realized she had miscalculated and had no money left...
How much money did she start with?
AAA = The amount of money in CENTS that SirCumference had left + The number of DOLLARS that The Better Half started with.
Mathman came up with a four-digit number during the advanced math class that he was teaching. He told his class, “The second digit is two times as much as the first digit, and if you square the second digit, you get the third and fourth digits. The sum of all the digits is 13.”...
After seeing that it didn’t cause much trouble to the bright students who did their homework each and every night, he decided to check on how they did with exponents. He told them to divide the number they got by 2^4 (2 to the fourth power), and then subtract 4^3 (4 to the third power) after doing the division...
Whoever got the answer first would receive one of the Snickers bars that Mathman took from SirCumference’s cache of Snickers. The number that candy-loving Chris got is = BB.
Cutie Pi had her boat moored at low tide in the Atlantic Ocean. Her boat’s ladder has eight rungs above water level with the rungs 8 inches apart at low tide...
Later in the day at high tide, she comes back to check on her fishing poles hanging over the dock. After seeing there was nothing on them, she TNL More bait, hoping the fish wouldn’t take it this time without staying on the hook! Looking down at the water level, she saw the tide brought the water level up 5 feet. When she looked at her boat, how many rungs were above the water?
The number of rungs Cutie Pi saw is = C.
Stage 2 coordinates are inside of Stage 1.
2. Develop the math formulas that will solve the puzzle.
1. SirCumference's Candy
How much of the $9 did SirCumference have left after buying the post-it-notes, snickers bars, and gumdrops?
Start by defining the terms of the equations.
- E - Earnings
- P - Post-it Notes
- G - Gumdrops
- S - Snickers
- C - Candy Purchased
- X - Money left after purchases
Now lay out the equations that must be solved.
- E = 9
- P = 1/3(E) - This means 1/3 times E
- 7G = 2S, or 2S = 7G
- 7S + 13G = 1/4(P)
- 14S + 11G = C, or C = 14S + 11G
- 9 - P - C = X, or X = 9 - P - C
Solve the equations to find X.
- P = 1/3(E)
- P = 1/3(9) = 3
- P = 3
- 2S = 7G
- S = 7/2G
- S = 3.5G
- 7S + 13G = 1/4(P)
- 7(3.5G) + 13G = .25(3)
- 24.5G + 13G = .75
- 37.5G = .75
- G = .75 / 37.5 = .02
- G = .02
- 7S + 13G = 1/4(P)
- 7S + 13(.02) = .25(3)
- 7S + .26 = .75
- 7S = .75 - .26
- 7S = .49
- S = .49 / 7 = .07
- S = .07
- C = 14S + 11G
- C = 14(.07) + 11(.02)
- C = .98 + .22 = 1.2
- C = 1.2
- X = 9 - P - C
- X = 9 - 3 - 1.2 =
- X = 4.8
SirCumference had $4.80 left.
2. Better Half's CITO event
How much money did she start with?
Start by defining the terms of the equations.
- M - Money for party
- F - Food
- D - Drinks
- S - Supplies
Now lay out the equations that must be solved.
- F = .5M
- D = .5(M - F) + 10
- S = .5(M - F - D) + 10
- M - F - D - S = 0
Solve the equations to find M.
- F = .5M
- D = .5(M - .5M) + 10
- D = .5M - .25M + 10
- D = .25M + 10
- S = .5(M - .5M - .25M - 10) + 10
- S = .5(M - .75M - 10) + 10
- S = .125M - 5 + 10
- S = .125M + 5
- M - F - D - S = 0
- M = F + D + S
- M = .5M + (.25M + 10) + (.125M + 5)
- M = .5M + .25M + .125M +10 + 5
- M = .875M + 15
- .125M = 15 = 120
- M = 120
- F = .5M
- F = .5(120)
- F = 60
- D = .25M + 10
- D = .25(120) + 10
- D = 30 + 10
- D = 40
- S = .125M + 5
- S = .125(120) + 5
- S = 15 + 5
- S = 20
The Better Half started with $120
AAA = The amount of money in CENTS that SirCumference had left + The number of DOLLARS that The Better Half started with.
AAA = 480 + 120 = 600
AAA = 600
3. Mathman's four-digit number
...Mathman came up with a four-digit number during the advanced math class that he was teaching. He told his class, “The second digit is two times as much as the first digit, and if you square the second digit, you get the third and fourth digits. The sum of all the digits is 13.”...
Start by defining the terms of the equations.
- F - First Digit of number
- S - Second Digit of number
- R - Third Digit of number
- U - Fourth Digit of number
- X - The Third and Fourth Digits of the number
Now lay out the equations that must be solved.
- S = 2F
- S^2 = X (X represents a two digit number 'RU')
- F + S + R + U = 13
Example: The number 25 = ((10 x 2) + 5)
So in this case;
Since you have a system with only four equations but five unknowns, you will have to limit one of the variables to a know set of possibilities, using trial and error to solve. The easiest formula to work with is S = 2F.
To begin, each of the digits is a single character between 0 - 9. Since S = 2F, F is limited to the numbers 0 - 4. (If F = 5, then S = 10, which is a two digit number) Now we will test each value for F.
If F = 0;
If F = 1;
If F = 2;
Since the sum of the digits must = 13, F = 2 is one possible solution.
Solving for F = 3, results in the equation 3 + 6 + 3 + 6 = 18
Solving for F = 4, results in the equation 4 + 8 + 6 + 4 = 22
Since neither of these is a valid solution, the correct four-digit number is: 2416
...After seeing that it didn’t cause much trouble to the bright students who did their homework each and every night, he decided to check on how they did with exponents. He told them to divide the number they got by 2^4 (2 to the fourth power), and then subtract 4^3 (4 to the third power) after doing the division...
- X = 'RU' = (10R + U)
Since you have a system with only four equations but five unknowns, you will have to limit one of the variables to a know set of possibilities, using trial and error to solve. The easiest formula to work with is S = 2F.
To begin, each of the digits is a single character between 0 - 9. Since S = 2F, F is limited to the numbers 0 - 4. (If F = 5, then S = 10, which is a two digit number) Now we will test each value for F.
If F = 0;
- S = 2F
- S = 2(0) = 0
- S = 0
- X = S^2
- X = 0^2
- X = 0 (Represented as a two-digit number, this would be '00')
- R = 0
- U = 0
- F + S + R + U = 13
- 0 + 0 + 0 + 0 = 0
If F = 1;
- S = 2F
- S = 2(1) = 2
- S = 2
- X = S^2
- X = 2^2
- X = 4 (Represented as a two-digit number, this would be '04')
- R = 0
- U = 4
- F + S + R + U = 13
- 1 + 2 + 0 + 4 = 7
If F = 2;
- S = 2F
- S = 2(2) = 4
- S = 4
- X = S^2
- X = 4^2
- X = 16 (Represented as a two-digit number, this would be '16')
- R = 1
- U = 6
- F + S + R + U = 13
- 2 + 4 + 1 + 6 = 13
Since the sum of the digits must = 13, F = 2 is one possible solution.
Solving for F = 3, results in the equation 3 + 6 + 3 + 6 = 18
Solving for F = 4, results in the equation 4 + 8 + 6 + 4 = 22
Since neither of these is a valid solution, the correct four-digit number is: 2416
...After seeing that it didn’t cause much trouble to the bright students who did their homework each and every night, he decided to check on how they did with exponents. He told them to divide the number they got by 2^4 (2 to the fourth power), and then subtract 4^3 (4 to the third power) after doing the division...
Whoever got the answer first would receive one of the Snickers bars that Mathman took from SirCumference’s cache of Snickers. The number that candy-loving Chris got is = BB.
- BB = (2416 / 2^4) - 4^3
- BB = (2416 / 16) - 64
- BB = 151 - 64
- BB = 87
3. Cutie Pi's Trick Question
Cutie Pi had her boat moored at low tide in the Atlantic Ocean. Her boat’s ladder has eight rungs above water level with the rungs 8 inches apart at low tide...
Later in the day at high tide, she comes back to check on her fishing poles hanging over the dock. After seeing there was nothing on them, she TNL More bait, hoping the fish wouldn’t take it this time without staying on the hook! Looking down at the water level, she saw the tide brought the water level up 5 feet. When she looked at her boat, how many rungs were above the water?
The number of rungs Cutie Pi saw is = C.Since the boat rises and falls with the tide, the number of rungs that show will remain the same.
Therefore: C = 8
3. Put the Stage 1 solved coordinates together.
Stage 1 is located at the following coordinates:
N 44° 54.AAA’ W 089° 32. BBC
- AAA = 600
- BB = 87
- C = 8
N 44° 54.600, W 089° 32.878
4. Verify the solved coordinates.
GeoChecker - SirCumference's Challenge
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