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Calculation is a solitaire card game with a standard 52-card deck. Initially, cards A, 2, 3, and 4 of any suit are laid out as four foundations. The remaining 48 cards are piled up as the stock, and there are four empty tableau piles. The purpose of the game is to move all cards of the stock to foundations. The foundation starting with A is to be built up in sequence from an ace to a king. The other foundations are similarly built up, but by twos, threes, and fours from 2, 3, and 4 until a king is reached. Here, a card of rank *i* may be used as a card of rank *i* + 13*j* for *j* ∈ {0, 1, 2, 3}. During the game, the player moves (i) the top card of the stock either onto a foundation or to the top of a tableau pile, or (ii) the top card of a tableau pile onto a foundation. We prove that the generalized version of Calculation Solitaire is NP-complete.

- Publication
- IEICE TRANSACTIONS on Information Vol.E106-D No.3 pp.328-332

- Publication Date
- 2023/03/01

- Publicized
- 2022/10/31

- Online ISSN
- 1745-1361

- DOI
- 10.1587/transinf.2022FCL0002

- Type of Manuscript
- Special Section LETTER (Special Section on Foundations of Computer Science — Foundations of Computer Science Supporting the Information Society —)

- Category

Chuzo IWAMOTO

Hiroshima University

Tatsuya IDE

Hiroshima University

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Chuzo IWAMOTO, Tatsuya IDE, "Calculation Solitaire is NP-Complete" in IEICE TRANSACTIONS on Information,
vol. E106-D, no. 3, pp. 328-332, March 2023, doi: 10.1587/transinf.2022FCL0002.

Abstract: Calculation is a solitaire card game with a standard 52-card deck. Initially, cards A, 2, 3, and 4 of any suit are laid out as four foundations. The remaining 48 cards are piled up as the stock, and there are four empty tableau piles. The purpose of the game is to move all cards of the stock to foundations. The foundation starting with A is to be built up in sequence from an ace to a king. The other foundations are similarly built up, but by twos, threes, and fours from 2, 3, and 4 until a king is reached. Here, a card of rank *i* may be used as a card of rank *i* + 13*j* for *j* ∈ {0, 1, 2, 3}. During the game, the player moves (i) the top card of the stock either onto a foundation or to the top of a tableau pile, or (ii) the top card of a tableau pile onto a foundation. We prove that the generalized version of Calculation Solitaire is NP-complete.

URL: https://global.ieice.org/en_transactions/information/10.1587/transinf.2022FCL0002/_p

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@ARTICLE{e106-d_3_328,

author={Chuzo IWAMOTO, Tatsuya IDE, },

journal={IEICE TRANSACTIONS on Information},

title={Calculation Solitaire is NP-Complete},

year={2023},

volume={E106-D},

number={3},

pages={328-332},

abstract={Calculation is a solitaire card game with a standard 52-card deck. Initially, cards A, 2, 3, and 4 of any suit are laid out as four foundations. The remaining 48 cards are piled up as the stock, and there are four empty tableau piles. The purpose of the game is to move all cards of the stock to foundations. The foundation starting with A is to be built up in sequence from an ace to a king. The other foundations are similarly built up, but by twos, threes, and fours from 2, 3, and 4 until a king is reached. Here, a card of rank *i* may be used as a card of rank *i* + 13*j* for *j* ∈ {0, 1, 2, 3}. During the game, the player moves (i) the top card of the stock either onto a foundation or to the top of a tableau pile, or (ii) the top card of a tableau pile onto a foundation. We prove that the generalized version of Calculation Solitaire is NP-complete.},

keywords={},

doi={10.1587/transinf.2022FCL0002},

ISSN={1745-1361},

month={March},}

Copy

TY - JOUR

TI - Calculation Solitaire is NP-Complete

T2 - IEICE TRANSACTIONS on Information

SP - 328

EP - 332

AU - Chuzo IWAMOTO

AU - Tatsuya IDE

PY - 2023

DO - 10.1587/transinf.2022FCL0002

JO - IEICE TRANSACTIONS on Information

SN - 1745-1361

VL - E106-D

IS - 3

JA - IEICE TRANSACTIONS on Information

Y1 - March 2023

AB - Calculation is a solitaire card game with a standard 52-card deck. Initially, cards A, 2, 3, and 4 of any suit are laid out as four foundations. The remaining 48 cards are piled up as the stock, and there are four empty tableau piles. The purpose of the game is to move all cards of the stock to foundations. The foundation starting with A is to be built up in sequence from an ace to a king. The other foundations are similarly built up, but by twos, threes, and fours from 2, 3, and 4 until a king is reached. Here, a card of rank *i* may be used as a card of rank *i* + 13*j* for *j* ∈ {0, 1, 2, 3}. During the game, the player moves (i) the top card of the stock either onto a foundation or to the top of a tableau pile, or (ii) the top card of a tableau pile onto a foundation. We prove that the generalized version of Calculation Solitaire is NP-complete.

ER -