randRangeWeighted(3, 8, 1, 1 / 6) D_PARENT === 1 ? randRange(1, 2) : randRange(D_PARENT + 1, 2 * D_PARENT - 1) N_PARENT / D_PARENT randRange(3, 8) randRange(3, 8) randRangeExclude(2, 2 * D_OFFSPRING_1 - 1, [D_OFFSPRING_1]) randRangeExclude(2, 2 * D_OFFSPRING_2 - 1, [ D_OFFSPRING_2]) N_PARENT * getLCM(D_OFFSPRING_1, D_OFFSPRING_2) / D_PARENT
D_PARENT === 1 ? N_PARENT : mixedOrImproper(N_PARENT, D_PARENT) mixedOrImproper(N_OFFSPRING_1, D_OFFSPRING_1) mixedOrImproper(N_OFFSPRING_2, D_OFFSPRING_2) N_OFFSPRING_1 / D_OFFSPRING_1 N_OFFSPRING_2 / D_OFFSPRING_2 OFFSPRING_1 / PARENT OFFSPRING_2 / PARENT getLCM(D_OFFSPRING_1, D_OFFSPRING_2)

The starting block below is CODE_PARENT units long. Use the tools to the right to convert the starting block into both of the goal blocks that are CODE_OFFSPRING_1 units long and CODE_OFFSPRING_2 units long. You can see your progress as the current blocks.

Starting Block:

initSliceClone(["current_block_1", "current_block_2"]); init({range: [[0, 1], [0, 1]], scale: [ 500, 25]}); rectchart([1, 0], ["#e00", "#999"]);

Current Block 1:

init({range: [[0, 1], [0, 1]], scale: [500, 25]}); rectchart([1, 0], ["#e00", "#999"]);

Goal Block 1:

init({range: [[0, 1], [0, 1]], scale: [500 * ANSWER_1, 25]}); rectchart([1, 0], [BLUE, "#999"]);

Current Block 2:

init({range: [[0, 1], [0, 1]], scale: [500, 25]}); rectchart([1, 0], ["#e00", "#999"]);

Goal Block 2:

init({range: [[0, 1], [0, 1]], scale: [500 * ANSWER_2, 25]}); rectchart([1, 0], [ORANGE, "#999"]);
Cut Starting Block into
1 piece
Copy Current Block 1
1 time
Copy Current Block 2
1 time
[pieces, times['current_block_1'], times['current_block_2']]
pieces = guess[0]; times['current_block_1'] = guess[1]; times['current_block_2'] = guess[2]; updateGraphAndAnswer();
guess = guess.length ? guess : [1, 1, 1]; $('#pieces').text(plural(guess[0], 'piece'));$('#current_block_1_times').text(plural(guess[1], 'time')); \$('#current_block_2_times').text(plural(guess[2], 'time'));

The goal block 1 of length CODE_OFFSPRING_1 units can be rewritten as fraction(N_OFFSPRING_1, D_OFFSPRING_1).

The goal block 1 of length CODE_OFFSPRING_2 units can be rewritten as fraction(N_OFFSPRING_2, D_OFFSPRING_2).

Cutting the starting block into x pieces is the same as dividing it by x.

We want to cut the starting block into a piece that can be copied into both goal block 1 and goal block 2.

A

The least common denominator of D_OFFSPRING_1 and D_OFFSPRING_2 (the denominators of the goal blocks) is LCM. Therefore you can copy a block \dfrac{1}{LCM} units long to make both goal blocks.

To find the number of slices to cut the starting block into we solve for s in the following equation:

CODE_PARENT ÷ s = \dfrac{1}{LCM}

CODE_PARENT = \dfrac{1}{LCM}s

CODE_PARENT \cdot LCM = s

s = SLICES

We now have a resulting block that is \dfrac{1}{LCM} units long. Now we simply divide our goal blocks by this value to see how many times we need to copy the resulting block.

\color{BLUE}{c1 = \dfrac{N_OFFSPRING_1}{D_OFFSPRING_1} ÷ \dfrac{1}{LCM} = \dfrac{N_OFFSPRING_1}{D_OFFSPRING_1} \cdot LCM = N_OFFSPRING_1 * LCM / D_OFFSPRING_1}

\color{ORANGE}{c2 = \dfrac{N_OFFSPRING_2}{D_OFFSPRING_2} ÷ \dfrac{1}{LCM} = \dfrac{N_OFFSPRING_2}{D_OFFSPRING_2} \cdot LCM = N_OFFSPRING_2 * LCM / D_OFFSPRING_2}

Therefore the solution is to cut the starting block into SLICES pieces, copy current block 1 N_OFFSPRING_1 * LCM / D_OFFSPRING_1 times and current block 2 N_OFFSPRING_2 * LCM / D_OFFSPRING_2 times.