PIMSO 2025 - Mathematics - Primary 6 - National Round

If P, I, M, S and O are whole numbers, find $P+I\times M+S\times O$. $5.69=P+\dfrac{1}{I+\dfrac{1}{M+\dfrac{1}{S+\frac3O}}}$.

What is the biggest number of times 2 is a factor in the result of $\dfrac{30!}{10!}$? $n!=n\times(n-1)\times(n-2)\times\cdots\times1$.

The operation # is defined as $a\mathbin{\#}b=a^2-ab+b^2$. What is the value of $(7\mathbin{\#}1)\mathbin{\#}(6\mathbin{\#}3)$?

If you will arrange A, B, C and D in descending order, which is the largest? $A=9^8$, $B=27^5$, $C=81^4$ and $D=3^{20}$.

What is the smallest number that should be multiplied to 650 to make it a perfect square?

Find the sum of $\dfrac6{3\times9}+\dfrac6{9\times15}+\dfrac6{15\times21}+\cdots+\dfrac6{93\times99}+\dfrac6{99\times105}$.

How many counting numbers between $2^4$ and $2^8$ are divisible by 2, 5 or 7?

On the number line, the tick marks correspond to consecutive integers. What is the value of x?

A, B, and C are prime numbers and $A\lt B\lt C$ and A is the smallest prime number. What is the value of C in $3A+4B+5C=148$? Hint: Try small prime numbers for A and B, then solve for C accordingly.

Original choices: A. 29; B. 23; C. 19; D. 17.

Editorial note: Explain the source difficulty; no automatic answer is assigned.

What is the unit’s digit of the sum of the addition sentence below? $201^1+202^2+203^3+204^4+205^5+206^6+207^7+208^8+209^9$.

What is the value of A in $\dfrac A{1\times3}+\dfrac A{3\times5}+\dfrac A{5\times7}+\cdots+\dfrac A{97\times99}=1$?

If p is a prime number, how many factors does p × p × p × p have?

Three friends each draw 3 number cards from a tray containing cards numbered 1, through 9. Boy : The product of my numbers is 21. Jame : The sum of my 2 numbers subtracted from my largest number gives a difference of zero. Great : The sum of my numbers is 18. Who drew the card numbered 9?

Paula has a polyhedron. His friends ask him questions which he answered as follows: Patricia: Does your polyhedron have more than 6 faces. Paula: Yes. It has more than 6 faces. Patricia: Does it have two bases and more than 12 edges? Paula: Yes. It has two bases and more than 12 edges. Patricia: Does it have 16 vertices? Paula: You are correct! It has 16 vertices. How many edges does Paula’s polyhedron have?

In the circular sector below, PH, HL and LS are straight lines. Points P, H, L, and S lie on the circumference of circle O. $PH=HL$ and $\angle LSO=35^\circ$. Find $\angle HLS$.

In the figure above, a square is inscribed in a circle. If the area of the square is 32, what is the area of the shaded region?

A triangle has sides HL = 32 in, PH = 69 in, and PL = c in, where the third side c is a whole number. How many possible values of c are there?

The quadrilateral PHIL is divided into four regions as shown below. If the areas of $\triangle POH$, $\triangle POL$, and $\triangle LOI$ are 110 cm², 90 cm², and 126 cm², respectively, find the area of $\triangle HOI$.

How many more small triangles must be shaded so that $\dfrac5{16}$ of the large triangle PHL is shaded?

Two circles P and H overlap as shown below. $\dfrac16$ of circle P and $\dfrac18$ of circle H are shaded. If the shaded region is 5 cm², find the area of the unshaded portion of the figure.