Do you mean y = 8 - x, being a diagonal?
Thanks Ravvie, yes I do mean y = 8 - x .
My eye must have drop down halfway along the second line when I typed up my equations.
y = 2x
y = 8 - x
0 = 8 - 3x
I think that’s a great solution! One which eluded me. Did you manage to do a PowerPoint or other image? Your description was sufficient for me to visualise it though.
Young Mr R came up with this solution:
- Cut diagonals to create 4 triangles.
- Place 2 triangles back to back along longest edge to create a square.
- Cut diagonal to create 4 half-sized triangles.
- Give the two full size triangles to A and B, then give two of the half-sized triangles to C.
- The two remaining half-sized triangles can form a square (a quarter of the cake).
- Repeat steps 1 to 5…
I think he had spent too long watching me chop down pea sticks the other day.
However, he did not need to use his finger on the knife to create a measurement. Step 2 uses the corners of a square to create an exact half. You could use something similar to modify your solution if you wanted to completely avoid measuring devices. However, Mrs R likes it that your solution involves a small number of finite cuts. Less time cutting means more time for eating chocolate cake!
Actually, Mrs R’s birthday is tomorrow and I am baking the cake this morning. Thanks for your solution, it will ensure harmony in the R household!
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Repeat dashed sloping line for the righthand side etc.
Hope the diagrams are self-explanatory.
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Seems pretty clear to me.
A second dashed diagonal line in the left half would give a second point to ensure that the red line is correctly aligned. But that is just minor detail.
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a nice one, nonetheless !
Also your “Place 2 triangles back to back along longest edge to create a square.” to avoid fingering the knife 
Hopefully the diagrams and equations will also help others understand what I had in mind !
Thank you for the “like” Mike.
Hope you, and others, still enjoy a few of these teasers.
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My solution is not based on geometry or any other mathematics. Instead it is based on game theory developed over the years between three chocolate-loving teenage brothers.
Person A: “I will cut one-third, you (B) can choose to take it or give it to me and take the knife.”
Person who is now holding the knife: “I will cut the remainder in half, you (C) can choose which piece you want then I will take the remaining piece.”
Guaranteed exact thirds every time.
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Nice one Ravvie.
Reminds me of the basic “I’ll cut, you choose” process.
I told Mrs R that I would bake her cake with a maximum diameter (distance from any two points across the top) of 8 inches. She promptly decided it should be circular. Luckily she didn’t push for spherical!
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Yes, I’m enjoying them thanks Don. I had started drawing up the cake solution and was thinking along your lines, but got distracted before finishing. Keep them coming folks.
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Well, assuming that “tomorrow” is now “today” - HAPPY BIRTHDAY !!
And I hope you each manage to get exactly 1/3 of that wonderful cake.
Mrs R says thank you.
It’s quite easy to cut a circle into thirds, but Mrs R exclaimed “You’re not using a compass anywhere near my cake!” So I had to resort to the ‘I cut, you choose’ approach.
Mrs R had first choice, young Mr R second choice.
I don’t think it was exactly thirds. Clearly I need to practise more!
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Here’s a nice golden oldie [please don’t post answer too quickly!!]
Have a good weekend folks 
3 friends are splitting a £30 bill after a meal; each handover £10 to the waiter who heads off to get a receipt. At the till the waiter realizes the bill is wrong and it should only have been £25. Rather than trying to split £5 between the 3 people, the waiter decided to keep £2 and hands back £1 to each customer stating the bill was wrong and should only have been £27.
Therefore, the 3 customers have paid £27 in total, plus the £2 the waiter pocketed = £29. They originally handed over £30, so what happened to the remaining £1?
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It certainly is a goldie.
And I still think these oldies are the best.
Nice one Cluffy.