MathDB

5

Part of 2021 BMT

Problems(5)

BMT Discrete #5 - Adding Reverse Makes a Palindrome

Source:

11/29/2021
How many three-digit numbers abc‾\underline{abc} have the property that when it is added to cba‾\underline{cba}, the number obtained by reversing its digits, the result is a palindrome? (Note that cba‾\underline{cba} is not necessarily a three-digit number since before reversing, cc may be equal to 00.)
countingDigitsBmt
BMT 2021 Guts Round p5

Source:

10/7/2022
Anthony the ant is at point AA of regular tetrahedron ABCDABCD with side length 44. Anthony wishes to crawl on the surface of the tetrahedron to the midpoint of BC‾\overline{BC}. However, he does not want to touch the interior of face △ABC\vartriangle ABC, since it is covered with lava. What is the shortest distance Anthony must travel?
geometry
BMT 2021 Geometry #5

Source:

8/12/2023
Let circles ω1\omega_1 and ω2\omega_2 intersect at PP and QQ. Let the line externally tangent to both circles that is closer to QQ touch ω1\omega_1 at AA and ω2\omega_2 at BB. Let point TT lie on segmentPQ P Q such that ∠ATB=90o\angle AT B = 90^o. Given that AT=6AT = 6, BT=8BT = 8, and PT=4P T = 4, compute PQP Q.
geometry
BMT 2021 General p5

Source:

9/27/2023
Bill divides a 28×3028 \times 30 rectangular board into two smaller rectangular boards with a single straightcut, so that the side lengths of both boards are positive whole numbers. How many different pairs of rectangular boards, up to congruence and arrangement, can Bill possibly obtain? (For instance, a cut that is 11 unit away from either of the edges with length 2828 will result in the same pair of boards: either way, one would end up with a 1×281 \times 28 board and a 29×2829 \times 28 board.)
combinatorics
2021 BMT Algebra #5

Source:

3/10/2024
Compute the sum of the real solutions to ⌊x⌋{x}=2020x\lfloor x \rfloor \{x\} = 2020x. Here, ⌊x⌋\lfloor x \rfloor is defined as the greatest integer less than or equal to xx, and{x}=x−⌊x⌋ \{x\} = x -\lfloor x \rfloor.
floor functionalgebra