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SEED expert Mark Passolt offers this solution:
This problem has many answers; let us find one of them.
Since there are three cubes and we want to make the numbers add up to 100, we can start by choosing numbers close to 33.
Put 35 on the first cube. What numbers should you put on the other cubes? If you use 32 and 33, then all 3 numbers add up to 100 (35 + 32 + 33). Are there other numbers you could use? How about 31 and 34? (See how I made one number smaller and the other one bigger?) They still add up to 100 (35 + 31 + 34). And 35 + 29 + 36 works too.
The cubes now look like:
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Cube A
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Cube B
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Cube C
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35
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32
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33
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35
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31
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34
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35
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29
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36
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So we have three different ways to get 100.
With this arrangement of numbers are there other ways to get 100?
Since Cube A has only 35 on it, the other two cubes need to add up to 65. And for each number on Cube B, there is only one number that will go with it to add up to 65.
So there are only three cases to get 100.
Some of the sides of the cubes are empty. You need to fill them with two-figure numbers. If the numbers are a lot different than 33, you won't be able to combine them to get 100. You can try some really big two-figure numbers:
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Cube A
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Cube B
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Cube C
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35
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32
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33
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99
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31
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34
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98
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29
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36
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97
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96
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95
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94
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93
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92
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91
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90
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89
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Do you see how only the cases we looked at before can add up to 100? If any of the numbers are in the 80s or 90s, the total will be much larger than 100 (For example 35 + 32 + 92 = 159).
Here are some questions for you to think about:
Can you find more solutions? Instead of using big numbers to fill in the cubes, can you fill them in with smaller numbers? Could you use a mix of big and small numbers?
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