This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

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Found problems: 61

2003 JHMMC 8, 17
Tags: JHMMC
Find the largest divisor of $2800$ that is a perfect square.

2003 JHMMC 8, 15
Tags: JHMMC
Evaluate $\frac{100-99+98-97\cdots +4-3+2-1}{1-2+3-4\cdots +97-98+99-100}$.

2014 JHMMC 7 Contest, 9
Tags: factorial , JHMMC
Let $n!=n\cdot (n-1)\cdot (n-2)\cdot \ldots \cdot 2\cdot 1$.For example, $5! = 5\cdot 4\cdot 3 \cdot 2\cdot 1 = 120.$ Compute $\frac{(6!)^2}{5!\cdot 7!}$.

2014 JHMMC 7 Contest, 5
Tags: palindromes , JHMMC
A palindrome is a word that reads the same backwards as forwards, such as “eye”, “race car”, and “qwertyytrewq”. How many letters are in the smallest palindrome containing the letters b, o, g, t, r, and o, not necessarily in that order and not necessarily adjacent?

2003 JHMMC 8, 1
Tags: JHMMC
Jane has $4$ pears, $5$ bananas, $3$ lemons, $1$ orange, and $6$ apples. If she uses one of each fruit to make a fruit smoothie, what is the total number of fruits that she has left?

2003 JHMMC 8, 3
Tags: JHMMC , Percentage , ratios
On an exam with $80$ problems, Roger solved $68$ of them. What percentage of the problems did he solve?

2014 JHMMC 7 Contest, 21
Tags: probability , Kelvin the Frog , Alex the Kat , Great character of JHMMC , JHMMC
Kelvin the Frog and Alex the Kat play a game. Kelvin the Frog goes first, and they alternate rolling a standard $6\text{-sided die.} If they roll an even number or a number that was previously rolled, they win. What is the probability that Alex wins?

2003 JHMMC 8, 7
Tags: JHMMC
Yao Ming is $7\text{ ft and }5\text{ in}$ tall. His basketball hoop is $10$ feet from the ground. Given that there are $12$ inches in a foot, how many inches must Yao jump to touch the hoop with his head?

2014 JHMMC 7 Contest, 16
Tags: poet s strategy , Integers , JHMMC
The sum of two integers is $8$. The sum of the squares of those two integers is $34$. What is the product of the two integers?

2014 JHMMC 7 Contest, 24
Tags: steven the troll , 44 word names , JHMMC
When submitting problems, Steven the troll likes to submit silly names rather than his own. On day $1$, he gives no name at all. Every day after that, he alternately adds $2$ words and $4$ words to his name. For example, on day $4$ he submits an $8\text{-word}$ name. On day $n$ he submits the $44\text{-word name}$ “Steven the AJ Dennis the DJ Menace the Prince of Tennis the Merchant of Venice the Hygienist the Evil Dentist the Major Premise the AJ Lettuce the Novel’s Preface the Core Essence the Young and the Reckless the Many Tenants the Deep, Dark Crevice”. Compute $n$.

2014 Contests, 4
Tags: French and Spanish Courses , JHMMC
$27$ students in a school take French. $32$ students in a school take Spanish. $5$ students take both courses. How many of these students in total take only $1$ language course?

2003 JHMMC 8, 24
Tags: JHMMC
If $a + b = 13, b + c = 14, c + a = 15,$ find the value of $c$.

2003 JHMMC 8, 30
Tags: JHMMC
Calculate $1 + 3 + 5 +\cdots+ 195 + 197 + 199$

2003 JHMMC 8, 6
Tags: JHMMC
Compute $\frac{55}{21}\times \frac{28} 5\times \frac 3 2$.

2014 JHMMC 7 Contest, 26
Tags: AMC , MOP , AIME , USAMO , JHMMC , IMO
Alex is training to make $\text{MOP}$. Currently he will score a $0$ on $\text{the AMC,}\text{ the AIME,}\text{and the USAMO}$. He can expend $3$ units of effort to gain $6$ points on the $\text{AMC}$, $7$ units of effort to gain $10$ points on the $\text{AIME}$, and $10$ units of effort to gain $1$ point on the $\text{USAMO}$. He will need to get at least $200$ points on $\text{the AMC}$ and $\text{AIME}$ combined and get at least $21$ points on $\text{the USAMO}$ to make $\text{MOP}$. What is the minimum amount of effort he can expend to make $\text{MOP}$?

2003 JHMMC 8, 4
Tags: JHMMC , easy , very very easy , very easy , addition , elementary contest , solve equations
A number plus $4$ is $2003$. What is the number?

2014 JHMMC 7 Contest, 18
Tags: JHMMC
A $6\text{-year stock}$ that goes up $30\%$ in the first year, down $30\%$ in the second, up $30\%$ in the third, down $30\%$ in the fourth, up $30\%$ in the fifth, and down $30\%$ in the sixth is equivalent to a $3\text{-year stock}$ that loses $x\%$ in each of its three years. Compute $x$.

2003 JHMMC 8, 29
Tags: JHMMC
How many three-digit numbers are perfect squares?

2003 JHMMC 8, 12
Tags: JHMMC
Compute $\frac{664.02}{9.3}$.

2014 JHMMC 7 Contest, 19
Tags: JHMMC
Lev and Alex are racing on a number line. Alex is much faster, so he goes to sleep until Lev reaches $100$. Lev runs at $5$ integers per minute and Alex runs at $7$ integers per minute (in the same direction). How many minutes from the START of the race will it take Alex to catch up to Lev (who is still running after Alex wakes up)?

2003 JHMMC 8, 23
Tags: JHMMC , Connecting squares
Let $ABCD$ be a square with side length $8$. A second square $A_1B_1C_1D_1$ is formed by joining the midpoints of $AB,BC,CD\text{ and }DA$. A third square $A_2B_2C_2D_2$ is formed in the same way from $A_1B_1C_1D_1$, and a fourth square $A_3B_3C_3D_3$ from $A_2B_2C_2D_2$. Find the sum of the areas of these four squares.

2003 JHMMC 8, 28
Tags: JHMMC
How many of the positive divisors of $120$ are divisible by $4$?

2014 JHMMC 7 Contest, 8
Tags: hedgehog and his friends , JHMMC
A hedgehog has $4$ friends on Day $1$. If the number of friends he has increases by $5$ every day, how many friends will he have on Day $6$?

2014 JHMMC 7 Contest, 22
Tags: Noice manipulation , JHMMC , JHMMC 7
For how many positive integer values of $x$ is $4^x- 1$ prime?

2014 Contests, 3
Tags: two graph function , JHMMC , function
Let $a\# b$ be defined as $ab-a-3$. For example, $4\#5=20-4-3=13$ Compute $(2\#0)\#(1\#4)$.