Krillion Math Answers
Krillion Math answers here cover prime numbers and cubes from our practice bank. Each example shows how to narrow the range, test a candidate, and enter the result. Practise the rule first and then try it with the timer on.
How Krillion Math answers work
Krillion Math answers depend on the rule and numerical limits you are given.
These questions come from the free game on this site. Each timed prompt accepts one guess. Use the clue to recall a set, then choose an answer you can type confidently. The metres in the lists follow our practice scoring.
Name a prime number between 10 and 30.
Hint: Cross out multiples of 2, 3, and 5 first.
- 100 m: 11, 13.
- 250 m: 17, 19.
- 500 m: 23, 29.
The primes in this interval are 11, 13, 17, 19, 23, and 29. Check divisibility by 2, 3, and 5. A composite number below 30 must have a factor below 6, which makes those prime divisors sufficient. Twenty-one fails because 3 times 7 is 21, and 25 fails because it is 5 squared. When you are scoring one answer under a timer, 11 is fast to recognize. If you are aiming for a higher tier, verify 23 or 29 using the small divisors before you submit it.
Name a positive cube number smaller than 150.
Hint: Multiply the same positive whole number by itself three times.
- 100 m: 1, 8, 27.
- 250 m: 64.
- 500 m: 125.
Start with the positive whole numbers as bases. Their first five cubes are 1, 8, 27, 64, and 125. The next one is 216, which is above the limit. Zero is a cube, but the prompt asks for a positive number. Eight is 2 × 2 × 2. Sixty-four is 4 × 4 × 4. Be careful with 25, which comes to mind because it is a square. To test a candidate, try identifying the base and multiplying it three times rather than looking for a number you recognize.
How to verify Krillion Math answers quickly
Krillion Math answers are quicker to verify if you read the endpoints before calculating.
Check the range before the arithmetic
A number can satisfy the mathematical property and fail the bounds. Thirty-one is prime and 7 is prime. Neither belongs between 10 and 30. On the cube prompt, 216 has the right form but is too large. Read phrases such as smaller than, between, and positive before choosing a candidate. With a strict upper bound, a value equal to that boundary would be outside the set. In these two practice questions, the wording gives you a compact set that you can check systematically.
Use small factors for a faster prime check
If a number can be written as a product of two whole numbers larger than 1, one factor is at most its square root. In the interval from 10 to 30, the square root is less than 6. A factor of 4 would imply a factor of 2, which you already tested. Once you try 2, 3, and 5, you have covered the prime factors that can explain a composite in the range. To test 29, notice it is odd, its digits add to 11, and its last digit is 9. Those checks eliminate all three possibilities.
Distinguish squares from cubes
When a prompt says cube, start from a base and build the number as base × base × base. The sequence of squares begins 1, 4, 9, 16, and 25. The first few positive cubes are different, apart from 1. Sixty-four happens to be both a square and a cube, so remembering it as 8 squared doesn't disqualify it from the cube category. Verify it the other way as 4 cubed. This approach makes the classification less dependent on the sequence you first remembered.
Enter the value in a listed form
The practice checker accepts digits and the number-word forms listed for these two prompts. You can type 29 or twenty-nine because punctuation becomes a space and the written form is in the list. For 125, the written form is accepted with or without and. Expressions such as 5^3 describe how to compute the value, but the prompt asks for the value. Type 125. Extra words such as metres belong to the score display, so there is no need to add them to your answer.
Build a two-minute drill
Write the integers from 11 through 29 in one row. Cross out multiples of 2, 3, and 5, then check the six you have left against the first answer table. In a second row, write bases 1 through 6 and cube them. Draw a line after 125 to show where the practice limit cuts off the sequence. Now turn the lists over and try recalling one low-tier and one high-tier answer for each prompt. This exercise separates knowing the method from trying to reproduce a memorized list during a timed dive.
Know when to take the simpler score
Under the optional 25-second timer, you can answer with a number you can verify quickly. A clear 13 keeps your run going with 100 metres. If you can explain why 29 passes the divisor checks as quickly, it earns 500 here. The two numbers are equally prime. The score differs because of the practice tiers. Review the missed guesses after the run and try to identify whether the difficulty was finding a number, applying the boundary, or typing the answer in the form the game expected.
Review a miss by changing one condition
After a round, take a number you entered and ask what wording would make it right. Seven would work for a prompt on single-digit primes. Zero would work for a question asking for a non-negative cube below 150. Changing the condition tells you whether your arithmetic was sound but your reading was too quick. Then try an adjacent question on your own. List the positive cubes below 100 or name a prime between 20 and 30. Check the result against the reasoning above before you look at a list.
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