All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Numbers
Four Triangles (Posted on 2024-05-06) Difficulty: 3 of 5
Rob drew four right-angled triangles. The hypotenuse of his first triangle was also the shortest side of his second triangle; the hypotenuse of his second triangle was also the shortest side of his third triangle; the hypotenuse of his third triangle was also the shortest side of his fourth triangle. The length in millimetres of each side of each triangle was an integer less than 100.

What were the lengths of the shortest and the longest sides that Rob drew?

Note: Adapted from Enigma number 1779 which appeared in New Scientist on 2013.

See The Solution Submitted by K Sengupta    
Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
No Subject | Comment 5 of 7 |

https://mycharmai.com/ math problems, concise puzzles that challenge and inspire in equal measure. With just a few words, they encapsulate mathematical concepts and problem-solving skills. From algebraic equations to geometric puzzles, they stimulate critical thinking and creativity. In this succinct format, math becomes a thrilling adventure, inviting participants to unlock solutions and discover the beauty of numbers within the confines of brevity.

<button class="rounded-md p-1 text-token-text-tertiary hover:text-token-text-primary" style="border-width: 0px; border-style: solid; border-color: rgb(227, 227, 227); --tw-border-spacing-x: 0; --tw-border-spacing-y: 0; --tw-translate-x: 0; --tw-translate-y: 0; --tw-rotate: 0; --tw-skew-x: 0; --tw-skew-y: 0; --tw-scale-x: 1; --tw-scale-y: 1; --tw-pan-x: ; --tw-pan-y: ; --tw-pinch-zoom: ; --tw-scroll-snap-strictness: proximity; --tw-gradient-from-position: ; --tw-gradient-via-position: ; --tw-gradient-to-position: ; --tw-ordinal: ; --tw-slashed-zero: ; --tw-numeric-figure: ; --tw-numeric-spacing: ; --tw-numeric-fraction: ; --tw-ring-inset: ; --tw-ring-offset-width: 0px; --tw-ring-offset-color: #fff; --tw-ring-color: rgba(69,89,164,.5); --tw-ring-offset-shadow: 0 0 transparent; --tw-ring-shadow: 0 0 transparent; --tw-shadow: 0 0 transparent; --tw-shadow-colored: 0 0 transparent; --tw-blur: ; --tw-brightness: ; --tw-contrast: ; --tw-grayscale: ; --tw-hue-rotate: ; --tw-invert: ; --tw-saturate: ; --tw-sepia: ; --tw-drop-shadow: ; --tw-backdrop-blur: ; --tw-backdrop-brightness: ; --tw-backdrop-contrast: ; --tw-backdrop-grayscale: ; --tw-backdrop-hue-rotate: ; --tw-backdrop-invert: ; --tw-backdrop-opacity: ; --tw-backdrop-saturate: ; --tw-backdrop-sepia: ; --tw-contain-size: ; --tw-contain-layout: ; --tw-contain-paint: ; --tw-contain-style: ; font-feature-settings: inherit; font-family: inherit; font-size: 16px; font-variation-settings: inherit; font-weight: inherit; letter-spacing: inherit; line-height: inherit; margin: 0px; padding: 0.25rem; appearance: button; background-image: none; cursor: pointer; border-radius: 0.375rem;"><svg width="24" height="24" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-md-heavy"><path fill-rule="evenodd" clip-rule="evenodd" d="M11 4.9099C11 4.47485 10.4828 4.24734 10.1621 4.54132L6.67572 7.7372C6.49129 7.90626 6.25019 8.00005 6 8.00005H4C3.44772 8.00005 3 8.44776 3 9.00005V15C3 15.5523 3.44772 16 4 16H6C6.25019 16 6.49129 16.0938 6.67572 16.2629L10.1621 19.4588C10.4828 19.7527 11 19.5252 11 19.0902V4.9099ZM8.81069 3.06701C10.4142 1.59714 13 2.73463 13 4.9099V19.0902C13 21.2655 10.4142 22.403 8.81069 20.9331L5.61102 18H4C2.34315 18 1 16.6569 1 15V9.00005C1 7.34319 2.34315 6.00005 4 6.00005H5.61102L8.81069 3.06701ZM20.3166 6.35665C20.8019 6.09313 21.409 6.27296 21.6725 6.75833C22.5191 8.3176 22.9996 10.1042 22.9996 12.0001C22.9996 13.8507 22.5418 15.5974 21.7323 17.1302C21.4744 17.6185 20.8695 17.8054 20.3811 17.5475C19.8927 17.2896 19.7059 16.6846 19.9638 16.1962C20.6249 14.9444 20.9996 13.5175 20.9996 12.0001C20.9996 10.4458 20.6064 8.98627 19.9149 7.71262C19.6514 7.22726 19.8312 6.62017 20.3166 6.35665ZM15.7994 7.90049C16.241 7.5688 16.8679 7.65789 17.1995 8.09947C18.0156 9.18593 18.4996 10.5379 18.4996 12.0001C18.4996 13.3127 18.1094 14.5372 17.4385 15.5604C17.1357 16.0222 16.5158 16.1511 16.0539 15.8483C15.5921 15.5455 15.4632 14.9255 15.766 14.4637C16.2298 13.7564 16.4996 12.9113 16.4996 12.0001C16.4996 10.9859 16.1653 10.0526 15.6004 9.30063C15.2687 8.85905 15.3578 8.23218 15.7994 7.90049Z" fill="currentColor"></path></svg></button><button class="rounded-md p-1 text-token-text-tertiary hover:text-token-text-primary" style="border-width: 0px; border-style: solid; border-color: rgb(227, 227, 227); --tw-border-spacing-x: 0; --tw-border-spacing-y: 0; --tw-translate-x: 0; --tw-translate-y: 0; --tw-rotate: 0; --tw-skew-x: 0; --tw-skew-y: 0; --tw-scale-x: 1; --tw-scale-y: 1; --tw-pan-x: ; --tw-pan-y: ; --tw-pinch-zoom: ; --tw-scroll-snap-strictness: proximity; --tw-gradient-from-position: ; --tw-gradient-via-position: ; --tw-gradient-to-position: ; --tw-ordinal: ; --tw-slashed-zero: ; --tw-numeric-figure: ; --tw-numeric-spacing: ; --tw-numeric-fraction: ; --tw-ring-inset: ; --tw-ring-offset-width: 0px; --tw-ring-offset-color: #fff; --tw-ring-color: rgba(69,89,164,.5); --tw-ring-offset-shadow: 0 0 transparent; --tw-ring-shadow: 0 0 transparent; --tw-shadow: 0 0 transparent; --tw-shadow-colored: 0 0 transparent; --tw-blur: ; --tw-brightness: ; --tw-contrast: ; --tw-grayscale: ; --tw-hue-rotate: ; --tw-invert: ; --tw-saturate: ; --tw-sepia: ; --tw-drop-shadow: ; --tw-backdrop-blur: ; --tw-backdrop-brightness: ; --tw-backdrop-contrast: ; --tw-backdrop-grayscale: ; --tw-backdrop-hue-rotate: ; --tw-backdrop-invert: ; --tw-backdrop-opacity: ; --tw-backdrop-saturate: ; --tw-backdrop-sepia: ; --tw-contain-size: ; --tw-contain-layout: ; --tw-contain-paint: ; --tw-contain-style: ; font-feature-settings: inherit; font-family: inherit; font-size: 16px; font-variation-settings: inherit; font-weight: inherit; letter-spacing: inherit; line-height: inherit; margin: 0px; padding: 0.25rem; appearance: button; background-image: none; cursor: pointer; border-radius: 0.375rem;"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M7 5a3 3 0 0 1 3-3h9a3 3 0 0 1 3 3v9a3 3 0 0 1-3 3h-2v2a3 3 0 0 1-3 3H5a3 3 0 0 1-3-3v-9a3 3 0 0 1 3-3h2zm2 2h5a3 3 0 0 1 3 3v5h2a1 1 0 0 0 1-1V5a1 1 0 0 0-1-1h-9a1 1 0 0 0-1 1zM5 9a1 1 0 0 0-1 1v9a1 1 0 0 0 1 1h9a1 1 0 0 0 1-1v-9a1 1 0 0 0-1-1z" clip-rule="evenodd"></path></svg></button><button class="rounded-md p-1 text-token-text-tertiary hover:text-token-text-primary" style="border-width: 0px; border-style: solid; border-color: rgb(227, 227, 227); --tw-border-spacing-x: 0; --tw-border-spacing-y: 0; --tw-translate-x: 0; --tw-translate-y: 0; --tw-rotate: 0; --tw-skew-x: 0; --tw-skew-y: 0; --tw-scale-x: 1; --tw-scale-y: 1; --tw-pan-x: ; --tw-pan-y: ; --tw-pinch-zoom: ; --tw-scroll-snap-strictness: proximity; --tw-gradient-from-position: ; --tw-gradient-via-position: ; --tw-gradient-to-position: ; --tw-ordinal: ; --tw-slashed-zero: ; --tw-numeric-figure: ; --tw-numeric-spacing: ; --tw-numeric-fraction: ; --tw-ring-inset: ; --tw-ring-offset-width: 0px; --tw-ring-offset-color: #fff; --tw-ring-color: rgba(69,89,164,.5); --tw-ring-offset-shadow: 0 0 transparent; --tw-ring-shadow: 0 0 transparent; --tw-shadow: 0 0 transparent; --tw-shadow-colored: 0 0 transparent; --tw-blur: ; --tw-brightness: ; --tw-contrast: ; --tw-grayscale: ; --tw-hue-rotate: ; --tw-invert: ; --tw-saturate: ; --tw-sepia: ; --tw-drop-shadow: ; --tw-backdrop-blur: ; --tw-backdrop-brightness: ; --tw-backdrop-contrast: ; --tw-backdrop-grayscale: ; --tw-backdrop-hue-rotate: ; --tw-backdrop-invert: ; --tw-backdrop-opacity: ; --tw-backdrop-saturate: ; --tw-backdrop-sepia: ; --tw-contain-size: ; --tw-contain-layout: ; --tw-contain-paint: ; --tw-contain-style: ; font-feature-settings: inherit; font-family: inherit; font-size: 16px; font-variation-settings: inherit; font-weight: inherit; letter-spacing: inherit; line-height: inherit; margin: 0px; padding: 0.25rem; appearance: button; background-image: none; cursor: pointer; border-radius: 0.375rem;"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" d="M3.07 10.876C3.623 6.436 7.41 3 12 3a9.15 9.15 0 0 1 6.012 2.254V4a1 1 0 1 1 2 0v4a1 1 0 0 1-1 1H15a1 1 0 1 1 0-2h1.957A7.15 7.15 0 0 0 12 5a7 7 0 0 0-6.946 6.124 1 1 0 1 1-1.984-.248m16.992 1.132a1 1 0 0 1 .868 1.116C20.377 17.564 16.59 21 12 21a9.15 9.15 0 0 1-6-2.244V20a1 1 0 1 1-2 0v-4a1 1 0 0 1 1-1h4a1 1 0 1 1 0 2H7.043A7.15 7.15 0 0 0 12 19a7 7 0 0 0 6.946-6.124 1 1 0 0 1 1.116-.868"></path></svg></button>
<button class="rounded-md p-1 text-token-text-tertiary hover:text-token-text-primary" style="border-width: 0px; border-style: solid; border-color: rgb(227, 227, 227); --tw-border-spacing-x: 0; --tw-border-spacing-y: 0; --tw-translate-x: 0; --tw-translate-y: 0; --tw-rotate: 0; --tw-skew-x: 0; --tw-skew-y: 0; --tw-scale-x: 1; --tw-scale-y: 1; --tw-pan-x: ; --tw-pan-y: ; --tw-pinch-zoom: ; --tw-scroll-snap-strictness: proximity; --tw-gradient-from-position: ; --tw-gradient-via-position: ; --tw-gradient-to-position: ; --tw-ordinal: ; --tw-slashed-zero: ; --tw-numeric-figure: ; --tw-numeric-spacing: ; --tw-numeric-fraction: ; --tw-ring-inset: ; --tw-ring-offset-width: 0px; --tw-ring-offset-color: #fff; --tw-ring-color: rgba(69,89,164,.5); --tw-ring-offset-shadow: 0 0 transparent; --tw-ring-shadow: 0 0 transparent; --tw-shadow: 0 0 transparent; --tw-shadow-colored: 0 0 transparent; --tw-blur: ; --tw-brightness: ; --tw-contrast: ; --tw-grayscale: ; --tw-hue-rotate: ; --tw-invert: ; --tw-saturate: ; --tw-sepia: ; --tw-drop-shadow: ; --tw-backdrop-blur: ; --tw-backdrop-brightness: ; --tw-backdrop-contrast: ; --tw-backdrop-grayscale: ; --tw-backdrop-hue-rotate: ; --tw-backdrop-invert: ; --tw-backdrop-opacity: ; --tw-backdrop-saturate: ; --tw-backdrop-sepia: ; --tw-contain-size: ; --tw-contain-layout: ; --tw-contain-paint: ; --tw-contain-style: ; font-feature-settings: inherit; font-family: inherit; font-size: 16px; font-variation-settings: inherit; font-weight: inherit; letter-spacing: inherit; line-height: inherit; margin: 0px; padding: 0.25rem; appearance: button; background-image: none; cursor: pointer; border-radius: 0.375rem;"><svg width="24" height="24" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-md-heavy"><path fill-rule="evenodd" clip-rule="evenodd" d="M11.8727 21.4961C11.6725 21.8466 11.2811 22.0423 10.8805 21.9922L10.4267 21.9355C7.95958 21.6271 6.36855 19.1665 7.09975 16.7901L7.65054 15H6.93226C4.29476 15 2.37923 12.4921 3.0732 9.94753L4.43684 4.94753C4.91145 3.20728 6.49209 2 8.29589 2H18.0045C19.6614 2 21.0045 3.34315 21.0045 5V12C21.0045 13.6569 19.6614 15 18.0045 15H16.0045C15.745 15 15.5054 15.1391 15.3766 15.3644L11.8727 21.4961ZM14.0045 4H8.29589C7.39399 4 6.60367 4.60364 6.36637 5.47376L5.00273 10.4738C4.65574 11.746 5.61351 13 6.93226 13H9.00451C9.32185 13 9.62036 13.1506 9.8089 13.4059C9.99743 13.6612 10.0536 13.9908 9.96028 14.2941L9.01131 17.3782C8.6661 18.5002 9.35608 19.6596 10.4726 19.9153L13.6401 14.3721C13.9523 13.8258 14.4376 13.4141 15.0045 13.1902V5C15.0045 4.44772 14.5568 4 14.0045 4ZM17.0045 13V5C17.0045 4.64937 16.9444 4.31278 16.8338 4H18.0045C18.5568 4 19.0045 4.44772 19.0045 5V12C19.0045 12.5523 18.5568 13 18.0045 13H17.0045Z" fill="currentColor"></path></svg></button>
<button class="btn relative btn-neutral btn-small popover shadow-lg" style="border-width: 1px; border-style: solid; border-color: var(--border-medium); --tw-border-spacing-x: 0; --tw-border-spacing-y: 0; --tw-translate-x: 0; --tw-translate-y: 0; --tw-rotate: 0; --tw-skew-x: 0; --tw-skew-y: 0; --tw-scale-x: 1; --tw-scale-y: 1; --tw-pan-x: ; --tw-pan-y: ; --tw-pinch-zoom: ; --tw-scroll-snap-strictness: proximity; --tw-gradient-from-position: ; --tw-gradient-via-position: ; --tw-gradient-to-position: ; --tw-ordinal: ; --tw-slashed-zero: ; --tw-numeric-figure: ; --tw-numeric-spacing: ; --tw-numeric-fraction: ; --tw-ring-inset: ; --tw-ring-offset-width: 0px; --tw-ring-offset-color: #fff; --tw-ring-color: rgba(69,89,164,.5); --tw-ring-offset-shadow: 0 0 transparent; --tw-ring-shadow: 0 0 transparent; --tw-shadow: 0 10px 15px -3px rgba(0,0,0,.1),0 4px 6px -4px rgba(0,0,0,.1); --tw-shadow-colored: 0 10px 15px -3px var(--tw-shadow-color),0 4px 6px -4px var(--tw-shadow-color); --tw-blur: ; --tw-brightness: ; --tw-contrast: ; --tw-grayscale: ; --tw-hue-rotate: ; --tw-invert: ; --tw-saturate: ; --tw-sepia: ; --tw-drop-shadow: ; --tw-backdrop-blur: ; --tw-backdrop-brightness: ; --tw-backdrop-contrast: ; --tw-backdrop-grayscale: ; --tw-backdrop-hue-rotate: ; --tw-backdrop-invert: ; --tw-backdrop-opacity: ; --tw-backdrop-saturate: ; --tw-backdrop-sepia: ; --tw-contain-size: ; --tw-contain-layout: ; --tw-contain-paint: ; --tw-contain-style: ; font-feature-settings: inherit; font-family: inherit; font-size: 0.875rem; font-variation-settings: inherit; font-weight: 500; letter-spacing: inherit; line-height: 1.25rem; margin: 0px; padding: 0.25rem 0.5rem; appearance: button; background-image: none; cursor: pointer; align-items: center; border-radius: 0.5rem; display: inline-flex; pointer-events: auto; position: relative; box-shadow: var(--tw-ring-offset-shadow,0 0 transparent),var(--tw-ring-shadow,0 0 transparent),var(--tw-shadow); --main-surface-primary: var(--white) !important; --main-surface-secondary: var(--gray-100) !important; --main-surface-tertiary: var(--gray-200) !important; --sidebar-surface-primary: var(--white) !important;">
<svg width="24" height="24" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-md"><path d="M7.5 13.25C7.98703 13.25 8.45082 13.1505 8.87217 12.9708C8.46129 14.0478 7.62459 15.5792 6.35846 15.76C5.81173 15.8382 5.43183 16.3447 5.50993 16.8914C5.58804 17.4382 6.09457 17.8181 6.6413 17.7399C9.19413 17.3753 10.7256 14.4711 11.169 12.1909C11.4118 10.942 11.3856 9.58095 10.8491 8.44726C10.2424 7.16517 8.92256 6.24402 7.48508 6.25001C5.55895 6.25805 4 7.82196 4 9.74998C4 11.683 5.567 13.25 7.5 13.25Z" fill="currentColor"></path><path d="M16.1799 13.25C16.667 13.25 17.1307 13.1505 17.5521 12.9708C17.1412 14.0478 16.3045 15.5792 15.0384 15.76C14.4917 15.8382 14.1118 16.3447 14.1899 16.8914C14.268 17.4382 14.7745 17.8181 15.3212 17.7399C17.8741 17.3753 19.4056 14.4711 19.8489 12.1909C20.0918 10.942 20.0655 9.58095 19.529 8.44726C18.9223 7.16517 17.6025 6.24402 16.165 6.25001C14.2389 6.25805 12.6799 7.82196 12.6799 9.74998C12.6799 11.683 14.2469 13.25 16.1799 13.25Z" fill="currentColor"></path></svg>
</button>
<form class="w-full" style="border: 0px solid rgb(227, 227, 227); box-sizing: border-box; --tw-border-spacing-x: 0; --tw-border-spacing-y: 0; --tw-translate-x: 0; --tw-translate-y: 0; --tw-rotate: 0; --tw-skew-x: 0; --tw-skew-y: 0; --tw-scale-x: 1; --tw-scale-y: 1; --tw-pan-x: ; --tw-pan-y: ; --tw-pinch-zoom: ; --tw-scroll-snap-strictness: proximity; --tw-gradient-from-position: ; --tw-gradient-via-position: ; --tw-gradient-to-position: ; --tw-ordinal: ; --tw-slashed-zero: ; --tw-numeric-figure: ; --tw-numeric-spacing: ; --tw-numeric-fraction: ; --tw-ring-inset: ; --tw-ring-offset-width: 0px; --tw-ring-offset-color: #fff; --tw-ring-color: rgba(69,89,164,.5); --tw-ring-offset-shadow: 0 0 transparent; --tw-ring-shadow: 0 0 transparent; --tw-shadow: 0 0 transparent; --tw-shadow-colored: 0 0 transparent; --tw-blur: ; --tw-brightness: ; --tw-contrast: ; --tw-grayscale: ; --tw-hue-rotate: ; --tw-invert: ; --tw-saturate: ; --tw-sepia: ; --tw-drop-shadow: ; --tw-backdrop-blur: ; --tw-backdrop-brightness: ; --tw-backdrop-contrast: ; --tw-backdrop-grayscale: ; --tw-backdrop-hue-rotate: ; --tw-backdrop-invert: ; --tw-backdrop-opacity: ; --tw-backdrop-saturate: ; --tw-backdrop-sepia: ; --tw-contain-size: ; --tw-contain-layout: ; --tw-contain-paint: ; --tw-contain-style: ; width: 768px;">
</form>

  Posted by Kate134 on 2024-05-08 14:15:05
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information