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Eric The Sheep Heath, Rainer, Nathan and Tom

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How We Figured It Out First off, we made a table of the answers up to 20, figuring the answers out by drawing them out. We saw a pattern emerge, for every three sheep in front of Eric, the number would increase

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FOR EVERY 1 SHEEP SHORN, ERIC WILL JUMP 2 SHEEP

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No. of sheep in front of Eric No. of sheep shorn before Eric 11 21 31 42 52 62 73 83 93 104 No. of sheep in front of Eric No. of sheep shorn before Eric 114 124 135 145 155 166 176 186 197 207

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Formula for 1 sheerer X 3 + 1 (except if the value of x is a multiple of 3, ie. 3, 6, 9, 12) You must only take the integer and leave out the decimal numbers. Example. 5/3+1= 2 Example. 12/3= 4

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A second formula A second formula we found to work was: if the number of sheep in front of Eric is a multiple of 3, simply divide by 3. If not, round the number up to the closet multiple of 3, ie. Round 19 up to 21 and divide by 3 to find 7, the answer.

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No. in front of Eric No. sheep shorn before Eric 104 155 114 124 135 207 83 10034 1000334

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Questions 2. Yes, You can predict it using the formula. All you have to do is round up to the next multiple of 3 and then divide by 3.

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3. If Eric was to jump 4 round up to to the next multiple of 4 and divide by 4. Same with method used with 5, just sub in 5 instead of 4

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FOR EVERY 3 SHEEP SHORN, ERIC WILL JUMP 2 SHEEP

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No. of sheep in front of Eric No. of sheep shorn before Eric 11 22 33 43 53 64 75 86 96 106 No. of sheep in front of Eric No. of sheep shorn before Eric 117 128 139 149 159 1610 1711 1812 1912 2012

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Pattern for 3 shearers A pattern emerged, “No. shorn before Eric,” goes up by 1, up by 1 again, then up by 1 and stay the same for the next 3, then repeats I.e. 1,2,3,3,3,4,5,6,6,6 The number at the end of the three same numbers created a ratio with the “No. in front of Eric,” of 5:3 I.e. 20:12, 15:9, 10:6 To figure out, round the “number in front of Eric” up to the next multiple of 5, then use the pattern to figure it out and count back

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Tried method 472 sheep in front of Eric, round up to 475, sub into ratio 5:3 475:285, divide down= 5:3 Count 285 back 3 places (475-472=3) answer is 282

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Thank You

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